mm 


The, mean  and  extreme  daily  Temperatures  in  St.  Louis 
for  forty-seven  years,  as  calculated  from  daily  obser- 
vations. 

Bv  Dr.  GEORGE  ENGELMANN. 


The  Evolution  of  the  amepj'^an  Trotting-Horse. 

By  FRANCIS  E.  in  J ''HER. 

Magnetic  Survey  of  Missouri.   5th  Annual  Report. 

By  FRANCIS  E.  NIPHER.       ' 

On  the  Expression  of  Electrical  Resistance  in 
Terms  of  a   Velocity. 

By  FRANCIS  E.  NIPHER. 


F'rom  the  Trans,  of  the.  St.  Louis  Acad,  of  Science.   Vol,  IV.,  JVo.  3. 
March,  1884. 


COMPLIMENTS  OF 

Francis  E.  JSripher. 


Digitized  by  tine  Internet  Arciiive 

in  2009  witii  funding  from 

Boston  Library  Consortium  IVIember  Libraries 


http://www.archive.org/details/meanextremedailyOOenge 


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THANS.   ST.  LOUIS  ACAD.  SCIENCE.  496 


Tlie  mean  and  extreme  daily  Temperatures  in  St. 
Louis  during  forty  seven  years,  as  calculated  from 
daily  observations, 

Bj   Dr.  George  Engelmann. 

Half  a  century  has  passed  since  I  began  to  study  the  meteor- 
ology and  climatology  of  this  neighborhood,  and  since  the  year 
1836  I  have  made  regular  meteorological  observations,  first  on 
temperature,  the  winds  and  the  condition  of  the  sky,  and  soon 
afterwards  on  atmospheric  pressure,  rainfall  and  humidity. 

I  give  here  the  results  of  my  thermometrical  observations, 
which  I  consider  as  the  most  important  and  most  interesting  of 
the  series.  They  comprise,  to  be  sure,  only  forty-seven  years,  and 
I  might  have  waited  until  at  least  half  a  century  was  completed  ; 
but  the  results  would  scarcely  have  been  different,  and  the  task 
then  perhaps  problematical  of  accomplishment. 

The  observations  were  made  within  the  city  of  St.  Louis,  and 
can  thus  not  claim  precision  for  this  whole  region.  St.  Louis, 
to  be  sure,  was,  when  they  commenced,  a  small  town  of  perhaps 
15,000  inhabitants,  while  now,  at  their  completion,  it  is  a  large 
city  of  probably  400,000,  with  the  necessary  accompaniment  of 
brick  and  stone,  and  especially  with  the  smoke  of  thousands  of 
chimneys,  furnaces  and  factories,  and  the  almost  total  absence  of 
verdure.  It  has  been  held  by  some,  that  these  influences  had 
little  effect  on  temperature,  but  that  brisk  breezes  would  soon  dis- 
pel smoke  and  equalize  temperature.  This,  however,  is  not  quite 
so,  and  direct  thermometrical  comparisons  prove  that  the  extreme 
temperatures,  and,  remarkably  enough,  even  the  extreme  heat, 
are  less  marked  in  the  city  than  in  the  country,  and  that  the  mean 
temperature  is  higher  in  the  city  than  in  the  country  (Trans,, 
vol.  ii.,  p.  yo)  ;  but,  aside  from  instrumental  observation,  the 
state  of  the  vegetation  proves  it  every  spring  and  fall,  when  we 
find  in  our  city  gardens  the  plants  uninjured  on  mornings  when 
in  the  country  they  have  suffered  from  late  or  early  frosts. 

St.  Louis  lies  very  nearly  in  the  centre  of  the  Mississippi  Valley, 
600  miles  north  of  the  Gulf  of  Mexico  and  just  as  far  south  of  Lake 
Superior,  about  500  miles  west  of  the  Alleghanies  and  800  miles 
east  of  the  Rocky  Mountains  ;    its  Washington  University,  one 


497      ENGELMANN MEAN  &  EXTREME  TEMPERAT'e  IN  ST,  LOUIS. 

mile  west  of  the  river,  lies  in  Lat.  38°  38'  03"  and  Long.  90°  12' 
15'' ;  the  low-water  mark  of  the  Mississippi  is  379  feet  above  the 
Gulf,  and  the  foot  of  Market  street  (City  Directrix)  is  413  feet 
above  the  same. 

My  observations  were  made  in  the  first  twelve  years  on  the 
south-east  corner  of  Second  and  Chestnut  streets,  only  two  blocks 
from  the  river  and  75  feet  above  low-water  mark  of  1863  ;  for  the 
next  22  years  on  the  south-west  corner  of  Fifth  and  Elm  streets, 
five  blocks  from  the  river  and  1 10  feet  above  low-water  mark  ; 
and  for  the  last  13  years  on  the  north-west  corner  of  Thirtieth  and 
Locust  streets,  two  miles  from  the  river  and  177  f"2et  above  low- 
water  mark.  When  1  was  absent  from  the  city  Dr.  A.  Wislize- 
nus  and  lately  Mr.  B.  D.  Kribben  have  kindly  filled  the  gaps. 

My  instruments  were  at  first  such  as  could  then  be  obtained 
here  ;  soon  I  imported  correct  thermometers  from  Europe,  and  for 
nearly  40  years  I  used  those  made  by  Jas.  Green,  then  of  Balti- 
more, and  soon  afterwards  of  New  York. 

For  many  years  the  observations  were  made  at  different  peri- 
ods of  the  day,  and  especially  at  hours  when  the  extremes  might 
be  expected  to  occur,  viz.  at  sunrise  and  at  3  p.m.  ;  and  the  maxi- 
mums and  minimums  were  selected  from  all  of  them,  often  eight 
in  a  day,  at  whatever  hour  of  the  day  they  were  found.  Differ- 
ential thermometers  were  observed  only  since  the  last  i  2  years. 
Thus  I  may  not  always  have  noted  the  absolute  extremes  of  each 
day,  and  my  tables  can  claim  only  approximate  reliability  ;  I 
give  them  for  what  they  may  be  worth,  but  I  can  assure  my 
readers  that  they  furnish  a  record  elaborated  with  zeal,  conscien- 
tiousness, care  and  assiduity,  and  for  a  length  of  time  such  as 
probably  few  others,  if  any,  exist  in  this  valley. 

The  arrangement  of  the  tables  explains  itself  The  first  two 
columns  represent  the  means  of  the  47  minimum  and  of  the  47 
maximum  observations  made  on  each  day  of  the  year,  and  the 
third  column  the  mean  calculated  from  the  two  former.  The  next 
^'Min."  column  gives  the  lowest  and  the  "Max."  column  the  high- 
est temperature  ever  observed  on  that  day ;  the  column  of  years 
next  to  these  gives  the  year  in  which  these  extremes  did  occur. 
The  last  column  represents  a  supposed — or  estimated — true  mean 
for  the  day  after  eliminating  excessive  extremes. 

The  year  has  been  divided   into  73  periods  of  5  days  each,  the 


TRANS.  ST.  LOUIS  ACAD.  SCIENCE.  498 

means  of  which  are  printed  in  full-face  type,  to  distinguish  them. 
It  will  be  seen,  however,  that  the  means  of  these  periods  do  not 
progress,  rise  and  fall,  much  more  evenly  than  the  single  daily 
means;  compare,  e.g.,  the  mean  of  Jan.  31st  to  Feb.  4th,  which 
is  so  much  lower  than  the  mean  of  the  foregoing  or  the  following 
five  da3' s  that  one  might  suspect  a  regular  and  normal  decline  of 
temperature  in  these  days,  and  not  a  mere  accident. 

A  few  facts  must  strike  every  one  who  examines  the  ta- 
bles. The  first  is,  that  a  time  even  as  long  as  47  3'ears  fails  to 
give  us  anything  approaching  absolute  and  reliable  means  ;  and 
we  come  to  the  painful  conclusion,  that  observations  even  contin- 
ued for  double  that  time,  or  for  a  century,  may  not  yet  obtain  that 
desirable  object.  It  seems  that  the  excessive  extremes  of  one  or  of 
a  few  days  such  as  we  often  observe  in  our  climate  of  extremes, 
especially  in  the  winter  season,  will  influence — or,  I  may  say, 
vitiate — the  means  of  a  long  series  of  observations  ;  and  the  ques- 
tion with  me  arises,  whether  such  extremes  ought  not  to  be  elim- 
inated from  the  series,  and  thus  truer  means  be  obtained.  At  the 
same  time  we  may  justly  be  astonished  that  from  such  heteroge- 
neous data  so  much  order  and  system  result — which  gives  us 
hope  that  we  cannot  be  quite  on  the  wrong  track. 

Another  fact,  which  strikes  us  in  looking  over  the  tables,  is 
that  the  mean  temperatures  do  not  increase  and  decrease  evenly, 
but  sometimes  quite  rapidly,  and  at  other  times  they  may  become 
almost  stationary  for  a  time.  These  points  come  out  most  strik- 
ingly on  a  diagram  which  embodies  the  essential  parts  of  the 
results  and  shows  the  daily  progress  of  the  temperature.  Thus 
we  find  very  little  change  from  the  middle  of  December  to  the 
first  part  of  February,  though  the  temperature  proves  to  be  low- 
est from  January  4th  to  13th  ;  then  we  notice  a  rapid  rise  from 
Feb.  6th  to  20th,  a  slower  rise  to  the  middle  of  March,  then  a 
rapid  one  to  the  end  of  the  month  ;  in  the  forepart  of  April  a  slow 
and  after  the  middle  of  that  month  a  very  marked  one  ;  then  fol- 
lows a  tolerably  even,  at  last  quite  slows  rise  to  July  9th,  when 
between  this  date  and  the  iSth  the  greatest  elevation  of  the  curve 
is  obtained.  After  that  the  mean  temperature  falls  slowly  to  the 
middle  of  August,  followed  by  a  more  rapid  decline  to  the  end 
of  September  ;  after  a  slight  pause  in  the  first  week  in  October, 
a  more  rapid  fall  takes  place  for  the  following  two  weeks  and  a 


499 


ENGKLMANN MEAN  &  EXTREME  TEMPERAT  E  IN  ST.  LOUIS. 


slighter  one  in  the  two  weeks  succeeding  them.  After  that  the 
temperature  sinks  rapidly  to  about  Dec.  loth,  from  which  time 
till  the  beginning  of  February  the  changes  are  not  very  marked. 

The  mean  temperature  of  April  17th  to  19th  and  from  October 
1 2th  to  17th  correspond  with  the  mean  of  the  year. 

The  tables,  and  still  more  distinctly  the  diagram,  show  us  also 
that  the  extreme  highest  and  lowest  temperatures  diverge  most  in 
winter  and  least  in  summer,  and  that  their  values  are  much  more 
variable  in  the  former  than  in  the  latter  season.  The  possibilities 
of  range  from  the  middle  of  December  to  the  iniddle  of  March  are 
80  to  95  degrees,  while  in  June  and  July  they  amount  only  to  40 
or  45  degrees. 

The  same  law  is  found  when  we  compare  the  actually  ob- 
served lowest  minimum  and  highest  maximum  of  every  month  ; 
their  divergence  is  greatest  in  January,  and  least,  not  much  more 
than  half,  in  July. 

Min,        Max.     Range. 

January —22.5      72.0  94.5 

February  ....   —15.0      76.0  91.0 

March 0.0  ■    86.0  86.0 

April 18.0       99.0  81.0 

May 29.0      97  5  68.5 

June 43.0    101.5  58.5 


Min. 

July 53.0 

August 45.0 

September  ...  35.0 

October 19.5 

November —  0.5 

December — 19 . 5 


Max.  Range. 

104.0  51.0 

104.0  59.0 

102.0  67.0 

91  0  71.5 

81.5  82.0 

72.5  92.0 


Nearly  the  reverse  is  the  case — i.e.  the  range  in  winter  is  much 
smaller  than  that  in  summer — if  we  compare  the  difference  of  the 
average  daily  minima  and  maxima  for  each  month  : 


January..  13.27 
February.  14.72 
March....   16.40 


April 18.29 

May 18.77 

June 18.14 


July 18.24 

August...  17.75 
September  19.05 


October  ..  18.00 
November  14.06 
December.  11.97 


The  range,  it  will  be  seen,  is,  on  the  whole,  least  in  the  cooler 
and  greatest  in  the  warmer  months  of  the  year  ;  but  this  differ- 
ence is  not  due  to  the  lower  or  higher  temperatures  of  those 
months,  for  it  will  be  seen  that  in  December  the  range  is  the 
smallest  (smaller  than  in  January)  and  in  September  greatest 
(greater  than  in  July).  This  variation  in  the  range  of  maxima 
and  minima  is  undoubtedly  owing  to  the  condition  of  the  sky  in 
the  different  months.  Gloomy  weather  prevails  in  the  beginning 
of  winter,  and  a  clear  sky  with  abundant  evaporation,  and  thus 
a  reduction  of  night  temperature,  in  the  autumn.  The  little  table 
can  give  us  an  indication  of  the  prevailing  weather  in  the  differ- 
ent months.     Thus  the  difference,  and  its  cause,  the   clearness  of 


TRANS.  ST.  LOUIS  ACAD.  SCIENCE. 


500 


the  sky,  rises  from  December  gradually  till  May,  falls  a  little  in 
June  and  July  and  more  in  August,  rises  to  its  highest  point  in 
September,  is  yet  high  in  October  and  then  falls  rapidly  till  De- 
cember, to  rise  again  in  January. 

The  temperature  of  our  continental  locality  shows  a  great  dif- 
ference from  that  of  the  western  coast  of  Europe  ;  as  a  convenient 
example  we  may  refer  to  the  temperature  of  London.  Their  win- 
ters are  warmer  from  the  latter  part  of  November  until  the  begin- 
ning of  March,  and  their  summers  much  cooler  from  this  period  to 
the  latter  third  of  November  ;  and  the  mean  is  much  higher  here. 

Whole 
Jan.    Feb.  Mar.    Apr.    May.   June.    July..   Aug.    Sept.    Oct.    Nov.  Dec.  year. 

St.  Louis..  31.8  35.4  43.7  56.2  66.3  74.7  79.2  76.8  69.0  56.1  42.8  33.4  55.4 
London...  37.2  39.3  42.7  48.1  54.5  60.8  68.6  62.0  57.6  50.4  42.7  39.7  49.9 
Difference. -+5.4  +3.9  — LO  —8.1  -11.8  -13.9  —15.6  -14.8  -11.4  -5.7  -0.1  +6.3  -5.5 


MEAN  AND  EXTREME  TEMPERATURES  IN  ST.  LOUIS  FROM  1836  to  188?. 


Mean  Values  for  each 

Extreme  Maxima  and  Minima  observed      i 

Sup- 
posed 
true 

1836-1882 

Day. 

on  each  Day 

3f  the  Year.                      | 

Min.    1    Max.   1  Mean. 

Min. 

Year. 

Max. 

Year. 

Mean, 

Jan.  1 

23.55    36.77 

30.16 

—22.5 

1864 

68.0 

1876 

31.5 

2 

25.35 

37.97 

31.66 

—13.0 

1879 

65.5 

1855 

31.3 

3 

25.54 

38.55 

32.04 

—15.5 

(1 

66.5 

1874,  1880 

31.0 

4 

23.95 

35.82 

29.88 

—  6.0 

(< 

63.5 

1880 

30.5 

5 

23.45 

39.22 

31.33 

—  8.5 

1864 

62.0 

1876 

i  30.2 

24.36  37.66  31.01 

—  13.1 

65.1 

30.9 

6 

23.76 

37.63  1  30.69 

—  9.0 

1879 

64.0 

1880 

30.0 

7 

22.33 

33.95    28.14 

—  1.0 

1881 

64.0 

1839 

29.4 

8 

22.75 

.34.61    28.68 

—  6.0 

1877 

68.0 

1876 

29.0 

9 

22.65 

35.48    29.06 

—18.0 

1875 

65.5 

(( 

29.0 

10 

22.67 

34.82    28.74 

—11.0 

1881 

70.0 

1839 

29.5 

22.83 

35.29  29.06 

-9.0 

66.3 

29.4 

11 

25.42 

39.20    32.31 

—  1.0 

1881 

71.0 

1839 

i  30.0 

12 

26.69 

39.27     32.98 

—  2.0 

1852 

65.0 

1863 

i  30.2 

13 

24.61 

36.81     30.71 

0.0 

<( 

59.0 

i( 

30.6 

14 

25.61 

38.11     31  86 

—12.5 

1881 

64.0 

1848 

31.0 

15 

L'6.71 

39.67    33.19 

—  2.5 

1875 

66.0 

1847 

31.4 

25.80 

38.61  32.21 

—  60 

65.0 

30.6 

16 

24.03 

36.27    30.15 

2.0 

1841 

63.0 

1845 

31.8 

17 

21.09 

34.27  1  27.68 

—11.0 

(1 

64.0 

1842 

32.0 

18 

21 .65 

34.32    27.98 

—12.5 

1857 

66.0 

(( 

32.0 

19 

23.63 

38.09    30.86 

—12.0 

1852 

61.0 

1843 

32,0 

20 

27.83 

39.-54    33.68 

—  1.5 

1866 

64.0 

11 

32.0 

23.64 

36.49  30.07 

—  7.0 

63.6 

31.9 

21 

25.97 

.88.79    32.38 

—  3.0 

1854 

67.0 

1843 

1  32.0 

22 

23.84 

39.19    31. .52 

—  2.5 

1857 

62.0 

1858 

32.0 

23 

24.63 

38.36    31.49 

0.0 

1854 

62.0 

1864 

32.0 

24 

25.57 

39.64    32.60 

2.0 

1873 

65.0 

1860 

32.2 

25 

27.26 

41.63  34.44 

—  55 

1840 

65.0 

1864 

1  32.4 

2o.4o 

39.52 

32.48 

—  1.8 

64.2 

32.1 

50I       ENGELMANX  — 

-MEAN 

i-  EXTR 

.EME  TEMP 

ERAT 

E  IN  ST.  I. 

UUIS. 

Mean  Value  for  each 

Extreme  Maxima  and 

Minima  observed 

1  Sup. 

1836-1882 

Day. 

on  each  Day  of  the  Year. 

i  posed 

Min. 

Max.    1  Mean. 

Min. 

Year. 

Max. 

Year. 

Mean 

Jan.  26 

26.76 

40.36  . 

33.56 

1.0 

1865 

71.5 

1843 

:  32.6 

27 

26.96 

39.53 

33.24 

—  0.5 

1873 

72.0 

1864 

32.6 

28 

24.85 

39.15 

32.00 

—  6.5 

(( 

67.0 

i( 

'  82.7 

29 

25.32 

39  30 

32.31 

—23.0 

C( 

64.5 

1852 

32.8 

30 

24.79 

41.09 

32.94 

—  2.0 

1856 

64.5 

1842 

32.8 

25.73 

39.88 

32.81 

-6.2 

67.8 

32.7 

31 

24.96 

38.20 

31.58 

2.0 

1875 

65.5 

1877 

32.8 

Feb.  1 

23.32 

37.20 

30.26 

—  8.5  1 

1836 

70.0 

1854 

32.8 

2 

23.55 

35.77 

29.66 

—  3.5  i 

1873 

56.0 

1846 

32.9 

3 

21.71 

35.72 

28.72 

—15.0  1 

1856 

62.5 

1852 

1    32.9 

4 

22.01 

36.51 

29.26 

—11.0 

II 

61.0 

1837 

1  33.0 

23.11 

36.68 

29.89 

-7.2 

63.0 

32.9 

5 

24.67 

39.29 

31.98 

—  3.5 

1856 

61.0 

1837 

i!  33.0 

6 

26.00 

41  04 

33.52 

3.0 

1843 

67.0 

1855 

33.1 

7 

26.08 

41.19 

33.63 

—  3.5 

1872,  1875 

65.0 

1851 

33.1 

8 

24.74 

39.98 

32.36 

2.0 

1842 

66.0 

1847 

i    33.2 

9 

24.37 

40.05 

32.21 

—  5.0 

1875 

72.0 

1876 

I    33.3 

26.17 

40.31 

32.47 

-1.4 

66.2 

133.1 

10 

25.92 

41.56 

33.74 

1.0 

1841 

73.0 

1876 

■    33.5 

11 

29.98 

43.93 

36.95 

2.0 

(( 

73.0 

1845 

33.7 

12 

29.00 

43.44 

36.22 

2.0 

II 

70.5 

1882 

33.9 

13 

29.06 

40.41 

34.73 

4.5 

1838 

69.0 

1867 

34.0 

14 

24.71 

39.38 

32.04 

—  3.5 

1866 

64.0 

1857 

34.1 

27.73 

41.74 

34.73 

1.2 

69.9 

33.8 

15 

26.53 

41.09 

33.81 

—  9.5 

1866 

68.0 

1848 

34.2 

16 

26.07 

42.59 

34.33 

—  5.0 

[1 

63.5 

1857 

34.4 

17 

28.03 

41.18 

34.60 

—  4.0 

1838 

74.5 

11 

34.6 

18 

28.05 

42.39 

35.22 

—  2.5 

1849 

65.5 

1873 

34.8 

19 

30.26 

44.57 

37.41 

5.0 

1838 

76.0 

1859 

35.0 

27.79 

42.36 

35.07 

-  3.2 

69.5 

34.6 

20 

31.83 

45.80 

38.81 

—  3.5 

1870 

68.5 

1850 

35.5 

21 

30.33 

45.27 

37.80 

—  4.5 

1838 

68.0 

1836 

36.0 

22 

31.82 

46.97 

39.39 

1.5 

1858 

68.5 

1861 

36.5 

23 

30.11 

44.71 

37.41 

0.0 

1 . 

69.5 

1851 

37.0 

24 

29.38 

I  45.91 

37.64 

6.0 

1873 

69.0 

1880 

37.5 

30.69 

45.73 

38.21 

-0.1 

68.7 

36.6 

25 

31.02 

1  46.05 

38.53 

7.0 

1855 

67.0 

1876 

;i  38.0 

26 

31.68 

48.91 

40.29 

2.0 

1846 

68.5 

1880 

11  38.5 

27 

30.58 

45.46 

38.02 

5.0 

1836 

73.5 

1876 

38.7 

28'  30.47 

47.02 

38.74 

10.5 

1836,  1869 

74.0 

1861 

39.0 

Mar.  ll  32.35 

49.02 

40.68 

10.0 

1843 

79.5 

(1 

39.2 

31.22 

47.29 

39.25 

6.9 

72.5 

38.7 

2 

31.36 

45.97 

38.66 

8.0 

1843 

76.0 

1861 

39.8 

3 

29.29 

43.89 

36.59 

0.0 

1848 

78.0 

1842 

40.0 

4 

29.50 

44.54 

37.02 

6.0 

1875 

75.5 

1882 

40.5 

5 

30.62 

47.38 

39.00 

8.0 

1848 

71.0 

1855 

,  40.8 

6 

34.94 

49.20 

42.07 

i        4.5 

1869 

76.5 

1860 

41.0 

31.14 

46.19 

38.67 

1       5.3 

75.4 

40.4 

1 

34.88 

!  51.60 

43.24 

10.5 

1857 

77.0 

1853,  187J 

)     41.2 

i 

i  34.49 

1  50.31 

42.40 

13.5 

1875 

77.0 

1879 

41.4 

i 

>  35.01 

i  48.18 

41.59 

6.0 

1877 

78.5 

1842 

1  41.6 

1( 

)  33.22 

49.52 

41.37 

10.0 

1856 

79.5 

1279 

1  41.8 

11 

34.55 

!  49.67 

42.11 

7.0 

1836 

69.0 

1848 

42.0 

34.4? 

5  49.85 

42.14 

7.4 

76.0 

41.6 

TRANS.  ST.  LOUIS  ACAD.   SCIENCE. 


502 


j     Mean  Value  for  each 

1      Extreme  Maxima  and  Minima  observed        1 

Sup- 

1836-1882                     '^^y- 

for  each  Day 

3f  the  Year.                      | 

posed 

Min.        Max. 

Mean. 

Min. 

11.5 

Year. 

Max. 

Year. 

Mean 

Mar  12  34.82 

50.86 

42.84 

1836,  1857 

71.0 

1839,  1861  : 

42.2 

13  U.2i 

50.64 

42.44 

5.0 

1867 

75.0 

1850       1 

42.4 

14  34.51 

50.55 

42.53 

j        1.0 

ti 

76.5 

1875 

42.5 

15  33.87 

48.89 

41.38 

7.5 

1870 

80.5 

1854 

42.6 

16  34.14    50.03 

42.08 

9.0 

1843 

77.5 

1868 

42.8 

34.3150.19 

42.25 

6.8 

76.1 

42.5 

17  33.49 

52.07 

42.78 

10.5 

1879    . 

79.0 

1842 

43.0 

18  34.86 

52.32 

43.59 

15.0 

(< 

84.0 

II 

43.5 

19  36.09 

54.82 

45.45 

18.5 

1875 

84.0 

II 

44.0 

20  36.91 

52.52 

44.71 

14.0 

1855 

84.0 

11 

44.5 

21  34.21 

50.68 

42.44 

7.0 

1876 

76.0 

1878 

44.8 

35.11 

52.48 

43.79 

13.0 

81.4 

43.9 

22  35.56 

54.04 

44.80 

13.0 

1843 

76.0 

1857 

45.0 

23  37.09 

55.48 

46.28 

7.5 

II 

82.5 

1868 

45.2 

24  36.90 

54.30 

45.60 

1      12.0 

11 

83.0 

1842       i 

45.4 

25  37.21    53.76 

45.48 

1      13.0 

11 

82.5 

1852 

45.6 

26  37.69 

54.92 

46.30 

!      13.5 

1873 

78.5 

1838 

46.0 

36.89 

54.50 

45.69 

11.8 

80.5 

' 

45.4 

27  39.16 

56.81 

47.98 

23.5 

1850 

85.0 

1838        i 

46.5 

28  39.77    57.31     48.54 

18.0 

1855 

83.5 

1879        i 

47.0 

29  40.42    58.31 

49.36 

23.5 

1876 

86.0 

1842 

47.5 

30  41.07    57.91 

49.49 

28.0 

<i 

84.0 

1838 

48.0 

31   40.35    57.34 

48.84 

25.5 

1856 

84.0 

11 

48.5 

40.15  57.53  48.84 

23.7 

84.5 

47.5 

Apr.  1   39.70    57.25    48.47 

24.0 

1881 

81.5 

1882 

49.5 

2  40.92    61.12    51.02 

24.0 

(1 

85.0 

II 

50.0 

3  44.66    62.44 

53.55 

24.5 

1879 

86.0 

II 

51.0 

4  44.00    59.67 

51.83 

23.0 

11 

85.0 

11 

51.5 

5  42.79    60.82 

51.80 

22.5 

1857 

88.5 

1871 

52.0 

42.41  60.26 

51.33 

23.6 

85.2 

50.8 

6  43.61 

62.89 

53.25 

18.0 

1857 

89.0 

1871 

52.5 

7  44.77 

63.98    54.37 

29.0 

1880 

85.5 

1860 

53.0 

8  45.59 

60.96    53.28 

24.0 

1845 

82.5 

1836 

53.0 

9  43.84 

61.86    52.85 

27.0 

1857 

84.0 

1844 

53.2 

10  45.07 

61.94    53.50 

28.5 

1836,  1874 

87.0 

II 

53.4 

44.57 

62.33  53.45 

25.3 

85.6 

53.0 

11  43.81 

62.53    53.17 

27.0 

1857 

83.0 

1842 

53.6 

12  45.35 

62.44    53.89 

26.0 

II 

84  0 

1856 

53.8 

13  45.33 

63.59    54.46 

32.0 

11 

88.0 

1845 

54.0 

14  45.03 

63  26    54.14 

28.5 

11 

84.0 

'■• 

54.2 

15  44.52 

62.02    53.27 

23.0 

1850 

82.0 

1856 

54.4 

44  81 

62.7  7 

53.79 

27.3 

84.2 

54.0 

16  45.62 

62.26 

53.94 

26.5 

1875 

91.0 

1845 

54.6 

17  45.11 

h4.55 

54.83 

20.5 

11 

93.0 

1855 

55.0 

18  45.78    64.34 

55.06 

26.0 

11 

99.0 

II 

56.0 

19  47.20 

66.47 

56.83 

29.0 

1857 

83.0 

1847 

57.0 

20  48.47 

67.92 

58.19 

34.0 

II 

85.0 

1836 

58.0 

46.43 

65.11 

55.77 

27.2 

90.2 

56.1 

21   49  76 

69.01 

59.38 

36.0 

1857,  1875 

85.0 

1867 

59.0 

22  51.37 

69.70 

60.53 

i       31.5 

1875 

87.5 

1842 

60.0 

23  49.88 

69.90 

59.89 

i       31.5 

1865 

87.0 

1842,  1854 

60.0 

24  50.24 

68.92 

59.58 

34.0 

]        1874 

88.5 

1854 

60.0 

25  51.89 

70.82 

61.35 

33.5 

1874,  1875 

93  0 

1813,  1855 

60.0 

50.63 

69.67 

60.15 

33.3 

88.2 

59.8 

503      ENGELMANN MEAN  &   EXTREME  TEMPERAT  E  IN  ST.  LOUIS. 


Mean  Values  for  each   \ 

Extreme  Maxima  and  Minima  observed 

Sup- 

1836 1882 

Day. 

on  each  Day 

3f  the  Year. 

posed 

Min. 

Max. 

Mean.  1 

Min. 

Year. 

Max. 

Year. 

Mean 

Ap.  26 

51.20 

70.53 

60.86 

33.5 

1873 

88.0 

1872 

60.0 

27 

50.63 

69.98 

60.30 

37.0 

1857 

93.0 

1838 

60.0 

28 

51.21 

68.71 

59.96 

34.0 

1854 

83.5 

1845 

60.0 

29 

50.87 

69.15 

60.01 

33.0 

1874 

89.5 

i< 

60.0 

30 

50.68 

69.07 

59.87 

32.0 

1877 

92.5 

1855 

60.0 

50.92 

69.49 

60.20 

33.9 

89.3 

60.0 

May  1 

50.53 

69.72 

60.12 

35.5 

1877 

91.5 

1836 

60.0 

2 

51.06 

68.34 

59.70 

29.0 

1851 

87.0 

a 

60.2 

8 

51.05 

69.67 

60.36 

38.0 

1841 

88.5 

1849 

60.4 

4 

53.60 

71.04 

62.32 

37.0 

1877 

89.0 

1860 

61.0 

5 

53.72 

71.88 

62.80 

37.0 

1851 

91.5 

u 

6i.4 

51.99 

70.13 

61.06 

35.3 

89.5 

60.6 

6 

52.85 

71.47 

62.16 

37.5 

1863 

88.0 

1872 

61.8 

7 

53.77 

73  49 

63.63 

35.0 

1867 

88.0 

11 

62.0 

8 

54.05 

72.56 

63.30 

38.0 

1855 

88.0 

(( 

62.5 

9 

54.40 

73.21 

63.80 

39.0 

u 

88.0 

If 

63.0 

10 

53.37 

73.16 

63.26 

40.0 

1838,  1871 

89.5 

1844,  1863 

63.5 

53.68 

72.78 

63.23 

37.9 

88.3 

62.5 

11 

54.12 

72.78 

63.45 

39.0 

1864 

91.5 

1844 

64.0 

12 

55.17 

74.79 

64.98 

39.5 

1857 

91.5 

1836 

64.5 

13 

56.34 

75.17 

65.75 

,      41.5 

1878 

90.0 

1862 

65.0 

14 

56.72 

74.75 

65.73 

42.0 

u 

97.5 

1836 

65.5 

15 

55.61 

75.53 

65.57 

40.5 

11 

93.0 

(1 

66.0 

55.59 

74.60 

65.051 

40.5 

92.7 

65.0 

16 

56.73 

75.52 

66.12 

40.0 

1837,  1875 

92.0 

1851 

66.5 

17 

56.01 

73.47 

64.74 

42.0 

1857 

91.0 

1853 

67.0 

18 

55.19 

75.27 

65.23 

1      42.0 

" 

87.0 

1836,  1870 

67.5 

19 

57.24 

77.30 

67.27 

43.0 

1853 

89.5 

1871 

68.0 

20 

57.61 

77.34 

67.47 

42.0 

1852 

90.5 

1836 

68.2 

56.55 

75.78 

66.17 

41.8 

90.0 

67.4 

21 

58.76 

76.31 

67.53 

43.0 

1857 

96.0 

1870 

68.4 

22 

58.53 

78.02 

68.27 

40.0 

1838 

97.0 

(1 

68.6 

23 

59.26 

77.68 

68.47 

44.0 

1867,  1876 

90.0 

1839,  1856 

68.8 

24 

59.66 

78.80 

69.23 

45.0 

1851 

92.5 

1873,  1879 

69.0 

25 

60.21 

77.40 

68.80 

44.0 

1845 

93.0 

1860 

69.5 

59.28 

77.64 

68.46 

43.2 

93.7 

68.8 

26 

60.46 

81.00 

70.73 

48.0 

1853 

93.0 

1860 

70.0 

27 

60.33 

79.37 

69.85 

48.0 

(  ( 

94.0 

1874 

70.2 

28 

eo.46 

80.59 

70.52 

45.0 

1838 

91  0 

1848,  1851 

70.4 

29 

61.08 

79.24 

70.16 

44.0 

1866 

91.0 

1852,  1879 

70.6 

30 

61.68 

79.94 

70.81 

44.0 

1845 

90.0 

1841,  1854 

70.8 

60.80 

80.02 

70.41 

45.8 

91.8 

70.4 

31 

62.14 

79.25 

70.69 

52.0 

1856 

97.0 

1871 

71.0 

June  1 

61.49 

79.78 

70.63 

49.0 

1843 

91.0 

1845,  1852 

71.0 

2 

62.39 

80.70 

71.54 

49.0 

1838 

94.0 

1852 

i  71.2 

3 

62.44 

80.12 

71.28 

47.5 

1879 

93.0 

1856 

71.4 

4 

62.05 

79.06 

70.55 

44.0 

1859 

94.0 

1841 

71.6 

62.10 

79.78 

70.94 

49.3 

93.8 

71.2 

5 

61.36 

79.45 

70.40 

43.0 

1839 

93.0 

1871 

71.8 

6 

62.57 

81.88 

72.22 

43.0 

183S 

93.0 

1836.  1874 

72.0 

7 

62.18 

81.34 

71.73 

50.0 

1854 

95.0 

1874 

72.2 

8 

63.83 

81.95 

72.89 

49.0 

u 

96.0 

1836 

72.4 

9 

63.62 

81.18 

72.40 

51.5 

1852,  1877 

99.5 

(( 

!  72.6 

62.71 

81.16 

71.93 

47.3 

95.3 

72.2 

TRANS.  SI  .  LOUIS  ACAD.  SCIENCE. 


504 


Mean  Values  for  each 

Extreme  Maxima  an 

d  Minima  observed      1 

Sup- 

1836-1882 

Day. 

on  each  Day  of  the  Year. 

posed 
true 

Min. 

Max. 

Mean. 

Min. 

Year. 

Max. 

Year. 

Mean 

Jun.lO 

62.65 

81.90 

72.27 

46.5 

1877 

97.5 

1836 

72.8 

11 

61.90 

79.38 

70'.64 

45.0 

1842 

94.0 

1841 

73.0 

12 

63.32 

81.59  1  72.45 

50.0 

1858 

94.5 

lh53 

73.2 

13 

64.87 

83.82 

74.34 

50.0 

K 

94.5 

" 

73.4 

14 

65.01    83.84 

74.42 

51.0 

1856 

96.0 

1879 

73.6 

63.55  82.10 

72.82: 

48.5 

95.3 

73.2 

15 

65.11     83.79 

74.45 

49.0 

1869 

96.5 

1868 

73.8 

16 

65.26    82.32 

73.79 

53.0 

1841 

98.5 

u 

74.0 

17 

65.56    82.60 

74.08 

51.5 

1876 

98.5 

(1 

74.3 

18 

65.78    83.97 

74.87 

49.5 

u 

99.0 

n 

74.6 

19 

65.59    84.37 

74.98 

52.0 

1866 

96.0 

1853,  1869 

74.8 

65.46  83.41 

74.431 

51.0 

97.7 

74.3 

20 

65.92    83.96 

74.94 

52.0 

1862 

98.0 

1861 

75.0 

21 

65.57    83.52    74.54 

49.0 

1863 

97.0 

1853 

75.3 

22 

65.64    85.82 

75.73 

50.0 

1868 

99.0 

1871 

75.6 

23 

67.06    84.58 

75.82 

53.0 

u 

101.5 

(( 

76.0 

24 

66.91     85.11 

76.01 

55.5 

1853 

97.5 

1870 

76.5 

66.22  84.60 

75.41 

51.9 

98.6 

75.7 

25 

68.13    86.54 

77.33 

56.0 

1852 

98.0 

1870,  1882 

77.0 

26 

68.73    87.88 

78.30 

55.0 

1865 

98.5 

1870 

77.5 

27 

70.26    87.21 

78.73 

59.0 

1836 

97.0 

1854 

78.0 

28 

69.36    87.48 

78.42 

i      55.5 

1866 

100.0 

1870 

78.0 

29 

69.26    86.08 

77.67 

51.0 

u 

101.5 

11 

78.0 

69.15  87.04 

78.09 

55.3 

99.0 

77.7 

30 

69.23    86.95 

78.09 

56.0 

1871 

101.5 

1870 

78.0 

July  1 

68.39    85.91 

77.1fc 

54.0 

1851 

98.0 

1854 

78.0 

2 

68.06    85.60 

76.83 

54.0 

1861 

98.5 

1858 

78.0 

3 

68.42  ■  87.10 

77.76 

56.0 

1857 

99.5 

1856 

78.1 

4 

68.71    87.89 

78.30 

53.0 

1859 

100.5 

1868 

78.2 

68.56  86.69 

7  7.62 

54.6 

99.6 

78.1 

5 

69.24    87.39 

78.32 

56.5 

1882 

98.5 

1870 

78.3 

6 

70.11     88.05 

79.08 

54.0 

1842 

97.0 

1868 

78.6 

7 

70.20    87.84 

79.02 

58.0 

t( 

98.0 

1874 

79.0 

8 

70.55    87.97 

79.26 

58.0 

1870 

97.0 

1J:54,  1879 

79.0 

9 

71.05    89.15 

80.10 

57.0 

1842 

99.0 

1858 

79.2 

70.23  88.08 

79.15 

56.7 

97.9 

78.8 

10 

71.46    87.84 

79.65 

61.0 

1836 

101.5 

1881 

79.2 

11 

70.35    86.99 

78.67 

58.0 

1854,  1873 

100.0 

1841 

79.4 

12 

70.64    87.50 

79.07 

58.0 

1863 

100.0 

u 

79.4 

13 

69.99 

88.61 

79.30 

57.0 

1861 

100.6 

1862 

79.6 

14 

70.69 

88.66 

79.67 

56.5 

1882 

100.5 

1868 

79.6 

70.62 

87.92 

79.27 

58.1 

100.5 

79.4 

15 

71.44 

89.38 

80.41 

58.0 

1842 

100.0 

1856 

80.0 

16 

71.42 

89.02 

80.22 

55.0 

1863 

100.0 

1870 

80.0 

17 

70.66 

90.07 

80.36 

56.0 

u 

102.5 

1856 

80.0 

18 

70.77 

88.73 

79.75 

58.0 

1846 

101.5 

1868 

79.6 

19 

70.44 

87.70 

79.07 

1      58.0 

1878 

100.0 

1854 

79.4 

70.94 

88.98 

79.96 

57.0 

100.8 

79.8 

20 

69.94 

86.92 

78.43 

57.0 

1873 

100.5 

1854,  1860 

79.2 

21 

69.08 

86.42 

77.13 

57.0 

1869 

104.0 

1860 

79.0 

22 

68.63 

85.63 

77.94 

57.0 

1864 

101.5 

1870 

79.0 

23 

68.72 

87.16 

78.01 

55.0 

1861 

98.5 

(( 

79.0 

24 

69.01 

87.86 

78.43 

56.0 

11 

101.0 

(( 

78.8 

69.07 

86.79 

77.93 

56.4 

101.1 

79.0 

505       ENGELMANN- 

-MEAN 

r  &  EXTREME  TEMPERAT  E  IN  ST.  LC 

)UIS. 

Mean  Values  for  each 

Extreme  Maxima  and  Minima  observed       | 

Sup. 

1836-1882 

Day. 

on  each  Day 

of  the  Year.                     j 

posed 

Min. 

Max. 

Mean. 

Min. 

Year. 

Max. 

Year. 

Mean. 

Jul.  25 

70.24 

88.38 

79.31 

59.0' 

1876 

100.0 

1870 

78.6 

26 

70.73 

88.27 

79.50 

58.0  1 

1853 

99.5' 

u 

78.4 

27 

70.38 

87.58 

78.98 

56.0  i 

n 

101.5 

It 

78  2 

28 

70.23 

87.80 

79.01  1 

56.0 

(1 

100.0 

1838 

78.0 

29 

70.58 

87.58 

79.08  1 

61.0  ' 

1853,  1865 

101.0  1 

1854 

78.0 

70.43 

87.92 

79.17 

58.0 

100.4 

78.2 

30 

68.52 

85.57 

77.04 

55.0 

1847 

101.0 

1838 

77.8 

31 

67.96 

86.47 

77.21 

550 

1849 

100.0 

1854    ; 

77.8- 

Aug.l 

68.38 

87.33 

77.85 

52.0 

1842 

101.0 

i< 

77.5 

2 

68.25 

86.95 

77.60 

52.0 

u 

99.0 

1861       ! 

77.5 

3 

68.61 

86.59 

77.60 

55.0  ! 

u 

101.0 

" 

77.5 

68.34 

86.58 

77.46 

53.8 

100.4 

77.6 

4 

68.40 

85.51 

76.95 

54.0 

1880 

101.5 

1861       1 

77.5 

5 

68.50 

86.01 

77.25 

58.0 

(c 

97.5 

1858 

77.5 

6 

68.97 

87.18 

78.07  ; 

58.0  ' 

1842 

98.5 

1838 

77.5- 

7 

69.11 

87.07 

78.09 

57.5 

1852 

100.0 

1861 

77.4 

8 

68.96 

87.09 

78.02 

56.0 

1869 

99.0 

1850       I 

77.4 

68.79 

86.57 

77.68' 

56.7 

99.3 

1 

77.4 

9 

68.94 

85.14 

77.04  ; 

58.0 

1879 

104.0 

1881 

77.4 

10 

69.07 

83.39 

76.23 

55.5 

1882 

98.0 

1 

77.4 

11 

69.37 

86.44 

77.90 

57.0 

(f 

100.5 

If 

77.4 

12 

68.38 

86.47 

77.42  1 

56.0 

1868 

105.0 

u 

77.2 

13 

68.72 

86.08 

77.40  ' 

57.0 

1860 

101.5 

1850 

77.0' 

68.89 

85.50 

77.19 

56.7 

101.8 

77.3 

14 

68.49 

85.30 

76.89 

56.5 

1861 

98.5 

1857 

77.0 

15 

68.52 

85.39 

76.95  \ 

59.5 

a 

97.0 

1841 

76.9 

16 

67.48 

86.22 

76.89 

57.0 

1866  ' 

96.0 

1860 

76.8. 

17 

67.94 

85.54 

76.74 

54.0 

1855 

97.0 

1843,  1860  1 

76.7 

18 

68.03 

86.27 

77.15 

56.0 

1855,  1866 

99.5 

1850 

76.5 

68.09 

85.74 

76.91 

56.6 

97.6 

176.8 

19 

68.19 

85.25 

76.72 

56.0 

1855 

99.5 

1850 

76.4 

20 

66.88 

85.72 

76.30 

1      52.0 

1836 

99.0 

u 

76.3 

21 

67.87 

85.71 

76.79 

,      59.0 

1864 

97.0 

1869 

76.2 

22 

67.29 

84.67 

75.98 

51.0 

1837 

97.5 

1872 

76.0 

23 

66.31 

84.09 

75.20 

52.0 

1866 

97.5 

1869 

76.0' 

67.31 

85.09 

76.20 

54.0 

98.1 

76.2 

24 

66.63 

85.29 

75.96 

49.0 

1866 

97.0 

1872 

75.8. 

25 

66.38 

84.42 

75.40 

50.5 

a 

100.0 

ii 

,  75.5 

26 

67.02 

84.94 

75.98 

49.0 

1863 

98.5 

u 

,  75.3 

27 

65.88 

84.11 

74.99 

54.0 

1856 

97.5 

1838 

1  75.0' 

28 

65.37 

82.98 

74.17 

51.0 

1844 

97.5 

1881 

■  74.8 

66.25 

84.35 

75.30 

50.7 

98.1 

75.8 

29 

64.80 

83.05 

73.92 

'      49.0 

1863 

99.5 

1881 

74.5 

30 

64.55 

84.34 

74.44 

1      45.0 

u 

100.5 

1854 

74.3 

31 

65.45 

82.96 

74.20 

48.5 

li 

99.0 

1854,  1873 

74.2 

Sept.  1 

64.75 

83.69 

74.22 

50.0 

1849 

98.5 

1854 

74.0 

2 

65.08 

82.80 

73.94 

51.5 

1850 

102.0 

1864 

74.0 

64.93 

83.37 

74.15 

48.8 

99.9 

74.2 

3 

64.54 

83.00 

73.77 

51.0 

1863 

102.0 

1864 

74.0 

4 

65.10 

83.59 

74.34 

1      51.0 

1868 

100.0 

1881 

74.0 

5 

65.33 

82.15 

73.74 

1      50.0 

1859 

100.0 

u 

73.8 

6 

64.98 

81.84 

73.41 

51.5 

1848 

97.0 

u 

73.6 

7 

65.61 

83.17 

74.39 

52.0 

1849 

97.0 

iC 

73.4 

65.11 

82.75 

73.93 

51.1 

99.2 

73.7 

TRANS.  ST 

.  LOUIS 

ACAD.  SCT 

ENCK. 

5ot> 

Mean  "Values  for  each 

Extreme  Maxima  an 

d  Minima  observed      1 

Sup- 

1836-1882 

Day. 

on  each  Day  of  the  Year.                      | 

posed 
true 

Min. 

Max.      Mean. 

Min. 

Year. 

Max. 

Year. 

Mean 

Sept.  8 

64.48 

83.47    73.97 

49.5 

1849 

99.5 

1854 

73.0 

9! 

63.79 

80.63     72.21 

50.0 

1847,  1869 

93.5 

1841 

72.0 

10 

62.r>9 

79.95    71.27 

46.5 

1880 

96.5 

1842 

71.0 

11 

61.01 

78.90    69.95 

47.5 

1878 

94.0 

"          1 

70.2 

12 

60.69  , 

77.79    69.24 

46.0 

1839,  1878 

92.0 

1865 

70.0 

62.51 

80.15  71.33 

47.9 

95.1 

71.2 

13 

60.27  I 

77.85    69.06 

47.0 

1839,  1878 

93.0 

1851,  1864 

70.0 

14 

60.37 

79.16    69.76 

43.5 

1873 

93.0 

1846 

69.5 

15 

60.51 

77.88    69.19 

47.5 

1880 

88.0 

1849,  1862  ! 

69.0 

16 

60.76 

79.34    70.05 

47.0 

1842 

91.5 

1857 

69.0 

17 

60.54  1 

77.72    69.13 

40.5 

1868 

93.0 

1843,  1857 

68.5 

60.49 

78.39  69.44 

45.1 

91.7 

69.2 

18 

60.08 

78.29    69.18 

42.0 

1863 

92.5 

1867 

68.0 

19 

57.74 

75.91    66.82 

44.5 

(( 

92.0 

u 

67.0 

20 

55.76 

73.68    64.72 

39.0 

1875 

93.5 

1881 

66.0 

21 

55.50 

73.29    64.39  | 

39.5 

1866 

95.0 

1872       1 

66.0 

22 

55.39 

73.69    64.54  ; 

39.0 

1875 

92.0 

1881       ' 

65.8 

56.89 

74.96  65.93 

40.8 

93.0 

66.5 

23 

58.17 

76.82    67.49 

36.0 

1856 

92.0 

1881 

65.5 

24 

58.15 

76.23    67.19 

37.0 

(1 

92.5 

"          i 

65.0 

25 

57.09 

75.37    66.23  : 

42.0 

1879 

91.5 

1850 

64.8 

26 

54.61 

73.81    64.21  j 

40.0 

1875 

92.0 

1847 

64.5 

27 

54.87 

73.82    64.34  | 

41.5 

1871 

88.0 

1854 

64.3 

56.58 

75.21  65.89; 

39.3 

91.2 

64.8 

28 

54.37 

73.53    63.95 

36.0 

1839 

90.5 

1867 

64.0 

29 

54.17 

71.87    63.02 

35.5 

1846 

93.0 

1858 

63.5 

30 

52.59 

71.53    62.06 

35.0 

1851 

90.0 

a 

63.0 

Oct.    1 

54.64 

73.37    64.00 

36.5 

1856 

87.0 

1856        ! 

63.0 

2 

54.68 

73.74    64.21  i 

38.5 

u 

91.0 

1867 

63.0 

54.09 

72.81 

63.45} 

36.3 

90.3 

63.1 

3 

54.52 

73.55 

64.03 

33.0 

1840 

89.0 

1872 

62.5 

4i  52.29 

70.59 

61.44 

31.0 

1836 

88.5 

(( 

62.0 

5  52.18 

70.36 

61.27 

34.0 

a 

88.0 

1879 

1  61.5 

6 

52.52 

70.03 

61.27 

34.0 

1855 

88.5 

1852 

'  61.5 

7 

51.93 

70.62 

61.27 

34.0 

1873 

87.0 

1860 

i  61.0 

52.69 

71.03 

61.86 

33.2 

88.2 

61.7 

8 

51.70 

71.14 

61.42 

31.5 

1868 

85.0 

1856 

i  60.5 

9 

51.49 

70.66 

61.07 

36.5 

1842,  1864 

87.0 

1879 

i  60.0 

10 

51.26 

69.91 

60.58 

37.0 

1849 

86.0 

11 

59.5 

11 

49.98 

67.14 

58.56 

31.5 

1872 

86.0 

a 

59.0 

12 

48.73 

64.91 

56.82 

30.0 

1875 

87.0 

a 

58.5 

50.63 

68.75 

59.69 

33.1 

86.2 

59.5 

13 

45.99 

65.96 

55.97 

29.5 

1860 

81.5 

1879 

58.0 

14 

1  47.20 

65.24 

56.22 

29.5 

1872 

84.0 

1878    • 

57.5 

15 

I  46  88 

65.82 

56.35 

28.0 

1845 

84.5 

1881    • 

57.0 

16 

47.34 

65.64 

56.49 

27.0 

1838 

83.0 

1842    : 

56.0 

17 

46.80 

65.42 

56.11 

31.0 

1836,  1868 

83.0 

1839,  1842 

55.0 

46.84 

65.61 

56.23 

29.0 

83.2 

56.7 

18 

44.64 

60.55 

52.59 

34.5 

1875 

82.5 

1867 

54.5 

19 

'  42.70 

61.62 

52.16 

30.0 

1846 

84.0 

1837 

!  54.0 

20 

42.75 

62.31 

52.53 

24.0 

1836 

83.0 

1843 

53.5 

21 

1  44.60 

62.47 

53.53 

25.0 

<( 

84.0 

1837 

53.0 

22 

44.15 

61.47 

52.81 

30.0 

1869 

85.0 

a 

52.5 

43.77 

61.68 

52.72 

28.7 

83.7 

53.5 

507       ENGE    MANN — -MEAN  cV  EXTREME  TEMPERAT'e  IN  ST.  LOUIS. 


Mean  Values  for  each 

Extreme  Maxima  an 

d  Minima  observed 

Sup- 

1836-1882 

Day. 

on  each  Day- 

Df  the  Year.                     ] 
Max.            Year. 

posed 
true 

Min. 

Max. 

Mean. 

Min, 

Year. 

Mean 

Oct.  23 

43.41 

61.54 

52.47 

20.0 

1863 

79.5 

1839 

52.0 

24 

44.32 

60.64 

52.48  ; 

20.0 

u 

78.0 

1875 

51.8 

25 

42.51 

59.96 

51.23 

22.0 

1841 

78.5 

1882 

51.6 

26 

43.64 

60.56 

52.10 

21.5 

1862 

81.5 

1874 

51.4 

27 

42.15 

61.11     51.63 

26.0 

1869 

81.5 

1870 

51.0 

43.20 

60.76  51.98 

21.9 

79.8 

51.5 

28 

43.54 

60.56 

52.05 

27.0 

1873,  1878 

80.5 

1874 

51.0 

29 

43.71 

60.77 

52.24 

22.0 

1873 

81.5 

1875 

50.5 

30 

42.34 

57.28 

49.81 

26.5 

1863 

81.5 

1876 

50.5 

31 

39.75 

56.66 

48.20 

19.5 

a 

80.0 

(f 

50.0 

Nov.  1 

42.01  1  59.97 

50.99 

22.0 

1873 

78.0 

1842,  1876 

50.0 

42.27 

59.05 

50.66 

23.4 

80.5 

50.4 

2 

43.20 

58.00 

50.60 

30.5 

1848 

77.0 

1847 

60.0 

3 

41.11 

56.59 

48.85 

25.5 

1879 

75.5 

1859 

49.8 

4 

42.01 

58.66 

50.33 

23.0 

11 

80.0 

1850 

49.4 

5 

41.23 

55.70 

48.46 

25.0 

1865 

72.5 

1874 

49.0 

6 

38.91 

55.29 

47.10  1 

23.5 

1877 

73.0 

1874,  1878 

48.5 

41.2956.85 

49.07 

25.5 

75.6 

49.3 

7 

40.78 

57.55 

49.16 

24.0 

1856 

77.0 

1874 

48.0 

8 

40.30 

55.78 

48.04  ' 

11.0 

1838 

75.5 

1868 

47.0 

9 

37.43 

51.88 

44.66 

16.0 

1 1 

75.0 

1844 

46.0 

10 

39.03 

52.71 

45.87 

20.0 

li 

76.0 

'< 

45.5 

11 

40.23 

53.53 

46.88 

26.5 

1869 

81.5 

1837 

45.0 

39.55 

54.29 

46.92 

19.5 

7  7.0 

46.3 

12 

36.93 

51.66 

44.29  1 

17.0 

1859 

71.5 

1879 

44.5 

13 

36.66 

52.82 

44.74 

15.0 

IC 

79.0 

11 

44.0 

14 

36.67 

51.86 

44.26 

20.0 

1872 

71.5 

1855 

43.5 

15 

35.18 

50.01 

42.59 

18.0 

1838 

72.0 

1873        1 

43.0 

16 

36.11     49.60 

42.85  ! 

10.0 

u 

69.0 

1865 

42.0 

36.31 

51.19 

43.75 

16.0 

72.6 

43.4 

17 

35.55 

47.80 

41.67 

12.0 

1838 

69.0 

1853 

41.0 

18 

33.62 

45.58 

39.60 

6.0 

1880 

72.0 

(1 

40.5 

19 

31 .60    45.03 

38.31 

7.5 

u 

71.0 

II 

40.0 

20 

32.59    45.11 

38,85 

9.5 

1872 

72.5 

1837 

39.5 

21 

33.09  :  45.84 

39.46 

10.5 

1880 

69.0 

1841 

39.0 

33.2945.87 

39.58 

9.1 

70.7 

40.0 

22 

32.28  '  45.92 

39.10 

6.5 

1880 

71.0 

1843 

38.5 

23 

32.14    43.97 

38.05 

9.5 

1871 

69.0 

1867 

38.0 

24 

29.85    41.93 

35.89 

5.5 

I860 

65.5 

1850 

37.8 

25 

29.83  :  41.92 

35.87 

0.0 

1839 

64.5 

1856 

37.6 

26 

31.25  i  44.06 

37.65 

14.0 

II 

65.0 

1850 

37.4 

31.07 

43.5637.31 

7.1 

67.0 

■ 

37.6 

27 

31.44 

43.22 

37.33 

5.0 

1845 

67.0 

1870       i 

37.0 

28 

31.64 

44.05 

37.84 

—  0.5 

u 

72.0 

1864 

36.8 

29 

29.04 

42.76 

35.90 

2.0 

1872 

76.5 

II 

36.4 

30 

28.55 

42.98 

35.76 

6.5 

1845 

72.5 

1837 

36.0 

Dec.  1 

30.33    45.57 

37.95 

—  1.0 

1. 

72.5 

II 

36.0 

30.30  43.71 

36.95 

2.4 

72.1 

36.4 

2 

31.06 

44.95 

38.00 

4.0 

1876 

72.0 

1864 

35.8 

3 

30.61 

43.00 

36.80 

8.0 

1859 

61.0 

1842,  1873 

35.6 

4 

30.75 

42.18 

36.46 

—  2.5 

1871 

59.0 

1877 

35.4 

5 

29.45 

41.33 

35.39 

2.5 

(( 

61.0 

1879 

35.2 

6 

29.56 

41.88 

35.72 

3.5 

1859 

«)2.0 

1861 

35.0 

30.28 

42.67 

36.47 

3.1 

63.0 

35.4 

;oS 


TRANS.  ST,  LOUIS  ACAD.  SCIENCE. 


Mean  Values  for  each 

Extreme  Maxima  an 

d  Minima  observed 

Sup- 

1836 1882 

Day. 

on  each  Day  of  the  Year. 

posed 
true 

Min. 
"28.00 

Max. 

40.23 

Mean. 

34.11 

Min. 

Year. 

Max. 

Year. 

Mean 

Dec.  7 

—11.0 

1882 

63To" 

1851 

34.0 

8 

27.79 

39.11 

33.49 

—  4.0 

i( 

65.0 

1861 

33.5 

9 

25.07 

35.35 

30.21 

—  5.0 

1876 

74.5 

(( 

83.0 

10 

23.89 

36.06 

29.97 

0.0 

1868 

68.0 

K 

32.5 

11 

28.19 

37.61 

32.90 

—11.0 

u 

68.0 

1873 

32.0 

26.59 

37.67 

32.13 

—  6.2 

67.7 

33.0 

12 

25.54 

37.15 

31.34 

—  0.5 

1868 

68.5 

1877 

31.8 

13 

26.25 

36.70 

31.47  ! 

4.0 

1865 

62.5 

1881 

31.6 

14 

23.46 

33.79 

28.62  ; 

—  1.0 

a 

59.0 

1861 

31.4 

15 

23. .57 

33.46 

28.51 : 

—  2.5 

1851 

67.5 

1877 

31.2 

16 

24.29 

34.83 

29.56 

—  0.5 

i( 

62.0 

u 

31.0 

24.62 

35.18 

29.90 

-0.1 

63.9 

31.4 

17 

25.10 

36.91 

31.00 

—  2.5 

1875 

67.0 

1877       : 

31.0 

18 

25.76 

38.87 

32.31 

1.0 

1876 

69.0 

(1 

30.8 

19 

26.37 

38  10 

32.23 

0.5 

1863 

67.5 

"          1 

30.6 

20 

23  51 

35.84 

29.67 

—  2.0 

1871 

65.0 

ti 

30.4 

21 

24.84 

36.97 

30.90 

—  2.0 

1865 

66.0 

'( 

30.0 

25.11 

37.34 

31.22 

—  1.0 

66.9 

30.5 

22 

22.64 

33.86 

28.25 

—14.0 

1872 

62.0 

1877 

yo.o 

23 

22.51 

35.34 

28.92 

—  7.0 

1870 

61.0 

1875 

30.2 

24 

23.90 

36.62 

30.26 

—19.5 

1872 

66.0 

(1 

30.5 

25 

25.42 

37.95 

31.68 

—11.0 

u 

70.0 

1867 

31.0 

26 

25.63 

38.06 

31.84 

—  5.0 

<( 

65.0 

1875 

31.2 

24.02 

36.36 

30.19 

—11.3 

64.8 

30.6 

27 

26.47 

38.41 

32.-14 

—  6.0 

1872 

65.0 

1846 

31.3 

28 

26.34 

37.80 

32.07 

—  6.0 

1880 

59.0 

1862 

31.5 

29 

25.83 

37.49 

31.66 

—18.0 

i( 

64.0 

1851 

31.5 

30 

23.26 

36.73 

29.99 

—  8.0 

<( 

66.0 

1875 

31.5 

31 

24.25 

38.43 

31. '!4 

—10.5 

1863 

73.5 

it 

31.5 

25.23  37.77 

31.50, 

1  —  9.7 

65.5 

1 

31.5 

The  annexed  diagram,  for  the  construction  of  which  I  am  in- 
debted to  Dr.  G.  Hambach,  represents  the  principal  resuhs  of 
these  tables.  The  perpendicular  lines  divide  the  year  into  73 
periods  of  5  days  each,  while  the  horizontal  ones  mark  the  de- 
grees. The  central  full-faced  curve  indicates  the  Mean  Tempera- 
ture of  the  penthemeral  periods  of  the  47  years,  as  actually  found, 
while  the  dotted  line  represents  the  supposed  real  Mean  Temper- 
ature as  suggested  in  the  last  column  of  these  tables.  The  upper- 
most curve  shows  the  Highest  Temperatures  and  the  lowest  curve 
the  Lowest  Temperatures  observed  in  those  same  penthemeral 
periods  within  the  s  ime  number  of  years.  It  will  be  noticed  that 
while  the  points  of  Mean  Temperature  occupy  the  centre  of  each 
period,  the  Maxima  and  Minima  do  not  show  in  the  middle  of  the 
spaces,  but  on  that  one  of  the  5  days  of  the  period  on  which  they 
actually  did  occur. 


—■■I 

■■■■■■■■■■■■■■■■■■■■■I 

IBUHBIIBIBillBSBnHBaiBBI&Sl 
■■■■■■■■.^1 


■ 


■■^■■■■■■■■■■■■■■■i 

■!■■■■■■■■■■■■■■■ 
_  KaBHiMRBBnUBIH 


BBWl—IMMI 

12 


■■■Mil 

IMBil  —■■■■■■■■■■■ 

■■■■HHHHIHBBHBaBi 

■■■■■■■■■■■■■■HiiaB 

■■■■■■ilHHHiBaHliiin 

ummmmmssmamammmm 


■■■■■■■■■■^■■■■■■H 
■■—■■■■■■■■■MB 


■■■^■■■■■■■■■■HBaH 

IhSSHIEBIIBBII 


NIPHER EVOLUTION  OF  THE  AM.  TROTTING-HORSE. 


509 


The  Etiolution  of  the  American  Trotting- Horse. '^ 

By  Francis  E.  Nipher. 

In  the  American  Journal  of  Science  for  April,  1883,  Prof.  W. 
H.  Brewer  has  furnished  data  for  the  discussion  of  the  change  in 
speed  of  the  American  trotting-horse.  His  table  is  here  repro- 
duced. 

TABLE  SHOWING  THE  NUMBER  OF  HORSES  UNDER  THE  RESPECTIVE 

RECORDS. 


Prof.  Brewer  states  that  the  data  for  the  speeds  2  130  and  2  127 
are  very  unsatisfactory,  but  for  all  the  others  are  reasonably 
correct. 

On  taking  the  logarithms  of  all  the  numbers  A^of  horses  capa- 
ble of  trotting  a  mile  in  5  seconds,  it  results  that  the  plotted  val- 
ues of  log.  A'^  for  their  proper  dates  give  a  straight  line  for  each 
value  of  s.  For  the  speeds  5  of  2  :30  and  2  127  these  lines  are 
parallel  to  each  other,  and  the  lines  representing  the  remaining 

*  Read  May  7th,  18S3. 


:io 


TRANS.  ST.  LOUIS  ACAD.  SCIENCE. 


speeds  are  also  parallel  to  each  other,  but  the  two  groups  are  not 
parallel. 

For  the  first  set,  the  lines  can  be  represented  by  the  equation 

log  iV-=^' +0.0,5^, 
where  y4'  is  a  function  of  .y,  and  7"  is  estimated  in  years  from  any 
-arbitrarily  assumed  date. 
For  the  second  group. 

It  is  apparent  that  for  the  speed  of  2  130  and  2  127  the  values 
of  N  are  too  small,  for  the  reason  perhaps  that  in  earlier  years, 
when  this  was  called  good  time,  less  general  attention  was  paid 
to  the  breeding  of  trotters,  while  in  later  years,  as  this  became  a 
common  speed,  a  constantly  increasing  number  of  horses  of  this 
grade  have  been  used  as  roadsters  and  remained  undiscovered  in 
private  hands. 

These  plotted  lines  are  shown  in  Fig.  i.  It  is  clear  that  the 
intersection  of  any  one  of  these  lines  with  the  time  axis  determines 
the  date  when  this  speed  may  be  supposed  to  have  originated, 
or  when  N=  i,  and  that  this  determination  of  the  date,  based  as 
it  is  upon  a  number  of  observations  running  through  a  series  of 
years,  is  much  more  reliable  than  the  date  when  some  accident- 
ally arranged  trotting  match  revealed  the  fact  that  the  horse 
capable  of  making  this  speed  had  already  come. 

The  dates  for  the  origin  of  the  speeds  of  2  :i3  and  2:11  cannot 
yet  be  determined  very  accurately,  and  this  fact  is  to  be  remem- 
bered in  considering  the  discussion  which  follows. 

The  following  table  gives  the  values  of  s  in  seconds  and  the 
dates  for  the  origin  of  these  speeds,  determined  as  before  ex- 
plained. The  third  column  contains  the  change  in  speed  per 
3ear,  calculated  in  a  well  known  manner  from  alternate  differ- 
ences in  the  two  previous  columns. 


ds 

5. 

YEAR. 

dT 


1 45 

1854-0 

143 

1857-4 

0-571 

141 

1861.0' 

0-547 

139 

1864.7 

0-  500 

137 

1869.0 

O-506 

13s 

1872. G 

O-430 

133 

1878.3 

0-476 

131 

188I.0 

NIPHKR EVOLUTION  OF  THE  AM.  TROTTING-HORSE.         51I 

When  the  vakies  of  --^  are  plotted  with  the  simultaneous  val- 
ues of  s,  we  get  a  somewhat  irregular  series  of  points  shown  in 
Fig  2,  and  represented  fairly  well  by  the  equation 

The  constants  A  and  B  can  be  determined  graphically  with 
as  great  precision  as  the  nature  of  the  data  will  warrant. 
The  values  are  found  to  be 

A  =       1. 00 

^  =  +0-0110. 

and  the  differential  equation  (i)  becomes 

^=  —  i-oo+o-oiio^  -  -  (2) 

This  equation  being  put  into  the  form 

,_QO     =0-oiio  ^^^ 

S  9U.  g 

it  admits  of  direct  integration  as  follows, 

n 

/df 

■  0  1 1 0  / 
5-90.9  -^ 

So  T 

on  performing  the  indicated  operations 

/(5— 90.9)  =/(i-o_90.9)  H-o-oiio  7"o_o.oiio  7; 
where  s^   and    7^q   are  simultaneous  values  at  any  assumed  date. 
Placing  the  initial  values  in  a  single  term,  we  have 

/(5-9o.,)=  c-^r  -        -        (3) 

or  for  the  primitive  equation 

C-BT 

s  =  90-9 +  e  -  -  (4) 

where  e  is  the  Naperian  base. 

It  thus  appears  that  the  limiting  speed  of  which  the  trotting- 
horse  is  capable,  which  he  will  continually  approximate  and 
never  reach,  is  1:31.  This  follows  from  (2)  by  making  — ^  =  o, 
or  from  (3)  and  (4)  by  making  T=  00 . 


/ 


ds      ^  Q  /dT 


512 


TRANS.  ST.  LOUIS  ACAD.  SCIENCE. 


The  constants  B  and  C  are  best  determined  by  taking  the  lo- 
garithms of  (^_9i)  for  the  vaiious  vakies  of  5,  and  plotting 
them  on  the  time  axis.  These  values  are  given  in  the  following 
table  : 


5. 

5 — 91. 

log  (5—91) 

YEAR. 

T. 

5   calc. 

DIFF. 

1 45 

54 

1-732 

1854-0 

—  6.0 

144.8 

— 0.2 

143 

52 

1. 716 

IS.S7-4 

—  2.6 

142.9 

— CI 

141 

50 

1.699 

1861.0 

I.O 

140.9 

— Q.  I 

'39 

48 

1.6S1 

1864.7 

--4-7 
--9.0 

139.2 

+0.2 

137 

i^6 

1.663 

1 869 . 0 

137-2 

4-0.2 

135 

44 

1-643 

1872.6 

--12.0 

135-2 

-|-0.2 

133 

42 

1.623 

1878.3 

-18.3 

132.6 

-0.4 

131 

40 

1.602 

1881 -o 

— 21.0 

131-4 

+0.4 

The  constants  are  determined  by  well  known  graphical  meth- 
ods, and  it  is  thus  found  that  the  observations  are  represented  by 
the  equation 

log  (.s_9i)  =  1.703  -  O-0046  ^'  -  (5) 

where  the  logarithms  are  common,  and  T  is  estimated  in  years 
from  i860.  Substituting  in  (4)  the  values  of  T  for  the  dates  of 
the  above  table,  the  values  of  s  and  their  differences  from  the  ob- 
served values  of  s  have  been  determined  and  are  given  in  the 
final  column.  These  differences  are  seen  to  be  greatest  for  the 
later  dates,  where  the  possible  errors  are  known  to  be  greatest ; 
but  the  error  in  5-  even  here  coriesponds  to  an  error  of  only  a 
year  in  date,  which  is  certainly  within  the  error  of  observation. 

From  (5)  it  is  easy  to  determine  the  date  when  the  horse  will 
have  reached  within  one  second  of  the  limiting  speed.  Making 
s  =  92,  this  value  of  2" turns  out  to  be  370  years.  By  the  close 
of  the  present  century  the  time  of  trotting  a  mile  will  be  reduced 
to  2  :o4,  and  the  time  of  3  :oo  will  be  reached  in  the  year  191 2. 
But  they  indicate  that  the  trotting-horse  will  finally  be  able  to 
make  his  mile  in  a  time  not  differing  materially  from  the  time 
of  the  running-horse,  which  is  at  present  about  100  seconds. 
Whether  or  not  the  trotting-horse  will  finally  beat  the  running- 
horse,  as  the  present  results  seem  to  indicate,  it  is  perhaps  not 
possible  to  decide  at  present  with  the  insufficient  data  at  our 
command.  A  weighty  consideration  is  found  in  the  fact  that  a 
well  trained  trotter  carries  his  body  more  steadily,  or  with  less  of 
rise  and  fall,  than  the  racer,  and  this  may  possibly  result  to  the 


NIPHER EVOLUTION  OF  THE  AM.  TROTTING-HORSE. 


513 


final  advantage  of  the  trotting-horse  after  the  process  of  develop- 
ing and  adjusting  of  his  muscles  and  chest  shall  have  been  suffi- 
ciently carried  on,  so  that  the  contest  between  the  trotter  and  the 
racer  shall  have  been  reduced  to  a  matter  of  muscular  capacity. 

It  is  w^ell  known  that  some  herds  of  wild  horses  on  the  Texas 
plains  were  natural  pacers,  and  even  when  pushed  to  the  utmost, 
and  for  days  together,  by  the  best  running-horses,  the  greater  por- 
tion of  them  held  to  their  gait.  One  large  white  pacer  became 
widely  known  and  his  capture  was  often  attempted,  but  he  al- 
ways proved  more  than  a  match  for  the  best  horses  that  could  be 
brought  against  him. 

Whatever  may  be  said  about  the  particular  numerical  results 
of  this  discussion,  it  is  clear  that  the  trotting-horse  is  very  likely 
to  reach  a  much  higher  speed  than  has  been  heretofore  thought 
possible. 

Added  Nov.  7,  1883. 

In  the  November  number  of  the  American  Journal  of  Science 
Mr.  W.  H.  Pickering  has  criticised  the  method  of  reduction  used 
in  the  present  paper  (which  had  been  printed  from  advance 
sheets  in  the  July  number  of  that  journal),  and  has  reached  a  very 
different  conclusion  from  that  reached  in  the  present  paper. 

Mr.  Pickering  thinks  that  it  is  objectionable  to  determine  the 
value  of  — ^  by  taking  the  alternate  differences  in  s  and  7^,  and 
he  has  reduced  the  observations  by  taking  differences  between 
consecutive  values  in  the  table.  In  this  way  he  gets  the  values  of 
the  third  column  in  the  table  below. 


s. 

\ 

YEAR. 

ds 
'dT' 

ds        , 

dT        ^^^''^ 

e. 

145 
143 
141 

139 

^37 
135 

131 

1854.0 

1857-4 
1861.O 
1864.7 
1869.0 
1872.6 
1878.3 
1881.O 

0-59 
0-55 
0-54 
0.46 

0-55 
0-35 
0-7.5 

0-59 
0.56 

0.54 
0.51 
0.49 
0.46 
0.44 

0.0 

—  0.1 
0.0 

-0.4 
+  0.4 

—  1-4 

+  1.8 

ds 


Plotting  these  values  of  ~y=r  and  the  corresponding  values  of  s, 
he  then  goes  on  to  say  that  the  points  so  determined  may  be  rep- 


ds 


resented  by  a  curve,  such   that  the   value   of  --tt^-  increases  as  s 


dT 


514  TRANS.  ST.  I.OUIS  ACAD.  SCIENCE. 

diminishes,  and  thus  indicating  disturbing  causes  not  easily  dis- 
cussed. Assuming  that  a  straight  line  will  represent  the  values, 
he  determines  the  value  of  the  constants,  and  finds  that  the  line 
intersects  the  axis  of  ^  at  a  point  where  the  value  of  5  is  —  25. 
This  would  mean  that  the  limiting  speed  of  the  trotter  is  25  sec- 
onds less  than  no  time  at  all. 

When  making  his  first  discussion  of  the  subject,  the  writer  con- 

ds 
sidered  the  propriety  of  determining   the  value  of  -,„  by  means 

of  consecutive  differences,  and  unfortunately  rejected  the  method 
without  even  giving  it  a  trial,  for  the  reason  that  the  dates  iSSi.^ 
and  1878.3,  corresponding  to  the  values  131  and  133  of  s.  were 
very  imperfectly  determined.  It  was  clear  that  the  additional 
point  thus  secured  would  deserve  very  little  weight.  It  was 
thought  to  diminish  the  irregvilarity  of  the  line  by  combining  these 
with  previous  and  better  determined  dates.  Mr.  Pickering  has 
not  only  used  this  method  (which  properly  used  is  capable  of 
yielding  good  results),  but  he  has  given  equal  weights  to  the  val- 
ues of  -7!,  for  all  the  dates  in  the  table.     This  is  the  fatal  defect 

which  entirely  vitiates  the  conclusion  reached  by  him.  A  refer- 
ence to  Fig.  I  of  this  paper  will  show  that  for  the  earlier  dates 
from  1854.0  down  to  1872.5  the  graphically  determined  dates  dif- 
fer from  the  real  dates  when  the  record  was  actually  lowered  by 
from  one  to  two  years. 

It  will  also  be  seen  that  the  dates  1S78.3  and  i88i.(,  are  subject 
to  errors  which  may  be  as  great  as  two  years.  After  having  made 
a  preliminary  examination,  these  dates  might  indeed  have  been 
"adjusted"  so  as  to  make  them  agree  better  with  the  others,  but 
they  now  stand  exactly  as  they  did  when  first  made  and  before 
any  other  work  had  been  done.  It  is  clear  that  the  most  weight 
should  be  given  to  the  earlier  dates.  I  have  therefore  plotted  the 
new  values  of  ^|r  with  the  values  of  5,  and  have  drawn  the  line 
representing  the  values  so  as  to  give  most  weight  to  the  best  de- 
termined values.     The  equation  of  this  line  is 

^  =  — 1-24  +O-0 127  •^-         -         -         -         (6) 

From  this  equation  the  values  of  -^  were  calculated  as  given 

in  the  fourth  column  of  the  last  table.     The  fifth  column,  headed 

e,  gives  the  time  in  years   by  which  the  corresponding    time  in- 


NIPHER — EVOLUTION  OF  THE  AM.  TROTTING  HORSE.  515 

tervals  dT  must  be  increased  in  order  to  bring  Mr.  Pickering's 

values  of  — ^^  into  accordance  with  the  values   calculated  from 
dT 

the  above  equation.  In  this  case  the  intervals  are  supposed  to  be 
separately  adjusted.  If  the  later  dates  were  simultaneously  ad- 
justed or  changed  by  intervals  ranging  from  two-tenths  to  three- 
fourths  of  a  year,  the  values  of  -^  ,  which  Mr.  Pickering  pre- 
fers to  use,  would  agree  exactly  with  the  values  calculated  from 
the  last  equation.  Now  it  is  perfectly  clear  that  these  later  dates, 
and  particularly  the  last  two,  are  subject  to  just  such  errors  as  this. 

Whatever  these  values  of  -j=-  may  be  said  to  prove,  they  cer- 
tainly do  not  prove  that  my  results  as  before  published  are  absurd, 
and  they  do  not  indicate  a  limiting  speed  of  _  25  seconds.  If 
--^=  o,  the  limiting  speed  of  the  horse  is  found  to  be  98  seconds. 

I  desire  to  express  my  thanks  to  Mr.  Pickering  for  his  criti- 
cisms and  suggestions,  as  he  has  corrected  a  tendency  which  I 
had  begun  to  feel,  to  attach  too  much  importance  to  the  numeri- 
cal result  reached  ;  but  I  maintain  that  his  method,  correctly  ap- 
plied, gives  in  general,  substantially,  the  same  result  as  my  own. 
It  is  not  necessary  to  assert  that  this  result  is  really  correct  if  any 
person  feels  inclined  to  doubt  it,  because  at  present  it  is  not  pos- 
sible to  demonstrate  it  more  fully  than  has  been  done  in  the  pres- 
ent paper.  I  only  insist  that  it  is  not  wholly  unwarranted  by  the 
facts  which  we  now  know. 

Most  horsemen  seem  to  think  that  the  limiting  speed  of  the 
trotting-horse  will  be  somewhere  near  a  mile  in  120  seconds.  If 
this  were  true,  the  differential  equation  could  hardly  be  a  linear 
one.     The  equation 

ds 


where  /&  is  a  constant  and  L  is  the  limiting  speed,  would  how- 
ever be  in  harmony  with  this  view.  But  this  equation  gives  on 
integration  an  equation  of  the  form 


V-y  -  Z  =  C—A  T  .         .        .         -         (8) 

According  to  this  equation  the  horse  would  absolutely  reach 
the  limiting  speed  L  in  a  finite  time,  —  .  Practically  this  may  be 
true,  as  is  in  fact  shown  by  my  own  equation  (4),  so  that  some 
such  equation  might  really  represent  the  results  sufficiently  rear 


5l6  TRANS,  ST.  LOUIS  ACAD.  SCIENCE. 

for  all  practical  purposes.  But  the  relation  is  not  a  rational  one, 
since  it  cannot  be  supposed  that  the  horse  will  really  attain  his 
limiting  speed  in  a  finite  time.  After  he  had  come  within  a 
thousandth  of  a  second,  it  would  take  a  great  interval  of  time  to 
compass  the  next  millionth  of  a  second.  Furthermore,  this  equa- 
tion could  not  hold  for  values  of  Z"  greater  than  2^,  as  the  value 
of  s  would  then  begin  to  increase  according  to  equation  (8).  I 
therefore  claim  that  equation  (4),  in  all  probability,  represents 
the  relation  between  the  values  o(  s  and  T,  and  that  the  constants 
in  the  equation  will  be  determined  with  greater  and  greater  pre- 
cision as  the  data  becomes  more  and  more  complete. 


Magnetic  Survey  of  Missouri.    Fifth  Annual  Report. 

By  Francis  E.  Nipher. 

During  the  summer  of  1882  the  survey  was  continued  under 
the  same  auspices  as  in  the  previous  year.  The  friend  who  fur- 
nished the  entire  means  for  conducting  the  work  enlarged  upon 
his  former  bounty,  and  furnished  the  party  with  two  fine  spring- 
wagons  designed  with  reference  to  the  needs  of  camp  life,  and 
provided  with  all  needed  conveniences.  Two  paid  assistants, 
Messrs.  Joseph  Cunningham  and  Albert  Meyer,  were  also  sent 
with  the  expedition,  and  Mr.  Frank  Ringling  of  the  Sophomore 
class  accompanied  the  expedition  as  volunteer  assistant,  paying 
his  own  expenses. 

The  work  of  the  summer  was  interfered  with  in  a  serious  man- 
ner by  the  sickness  of  the  horses,  and  more  particularly  by  the 
horrible  condition  of  the  roads,  due  to  heavy  and  long-continued 
rains.  During  the  entire  summer  we  were  compelled  to  improve 
roads  and  fords,  and  to  build  bridges,  and  this  frequently  took 
up  a  quarter  of  our  time  during  an  entire  week.  This  made  it 
impossible  to  make  complete  observations  after  Aug.  7th,  as  we 
were  obliged  to  travel  every  day  in  order  to  reach  St.  Louis  with- 
in the  time  which  could  be  devoted  to  the  survey.  After  the 
above  date,  therefore,  only  declination  observations  were  made, 
the  magnetic  meridian  being  determined  from  the  morning  elonga- 


NIPHER 5*'^  ANN.  REP.  MAGNETIC  SURVEY  OF  xMISSOURI.       517 

tion  as  explained  in  the  previous  report.*  The  true  meridian 
was  in  nearly  all  cases  obtained  by  pole-star  observations,  but  the 
great  number  of  cloudy  nights  made  it  necessary  in  some  cases 
to  observe  at  other  times  than  at  elongation. 

A  description  of  the  stations  where  observations  were  made 
is  here  given,  the  numbers  being  continued  from  the  previous 
report. 

Station  \o\  —  Kirk-wood,  St.  Louis  Co.  Lat.  38°  36';  Ion.  90°  24' . 
In  the  orchard  of  H.  W.  Leffingwell,  128  feet  from  the  street  fence  on 
the  south,  and  150  feet  from  that  on  the  east.  Polaris  observation  on 
elongation. 

Station  102 — Gray's  Summit.,  Franklifi  Co.  Lat.  38°  29';  Ion.  40° 
49'.  On  the  Union  road  about  half  a  mile  to  the  S.W.  from  the  railroad 
crossing,  and  in  the  second  depression,  20  ft.  from  the  road,  and  on  the 
N.W.  side.     Polaris  obs.  on  elongation. 

Station  iot^— Newport,  Franklin  Co.  Lat.  38°  36';  Ion.  91°  06'.  In 
the  "old  town"  on  the  summit  of  a  small  ridge,  128  ft.  N.W.  from  the  N.W. 
corner  of  the  church.  A  large  elm  to  the  N.W.  across  the  small  water- 
course is  said  to  be  at,  or  very  near,  the  N.W.  corner  of  the  S.E.  qr.  of 
sec.  II,  tp.  44,  r.  2  W.     Polaris  obs.  on  elongation. 

Station  104 — On  the  farm  of  August  Goebel,  near  Newport.  Lat.  38° 
34';  Ion.  91°  06' .  The  station  was  within  a  few  feet  of  the  middle  point 
of  the  line  dividing  the  E.  half  of  the  S.W.  qr.  from  the  W.  half  of  the  S.E. 
qr.  of  sec.  15,  tp.  44,  r.  2  W.  Polaris  obs.  on  elongation.  In  this  imme- 
diate vicinity  Dr.  Goebel,  grandfather  of  the  present  owner  of  the  farm, 
had  established  two  magnetic  stations,  where  he  made  extended  and  care- 
ful observations.  The  original  records  of  this  work  were  given  to  the  U.  S. 
Coast  Survey  some  years  since  by  his  son,  Mr.  Gert  Goebel. 

The  earlier  station  of  Goebel  is  found  by  going  from  our  station  in  a 
line  bearing  S.  93°  34'.5,  E.  255  ft.  and  thence  N.  83  ft.  This  station  of 
Goebel's  is  61  ft.  W.  and  14  ft.  N.  of  the  S.W.  corner  of  the  house  of  Au- 
gust Goebel.  The  observations  here  were  made  in  the  year  1839.  The 
declination  was  9°  21'  E. 

The  other  station  of  Dr.  Goebel  was  occupied  in  the  year  1849.  ^t  is  at 
the  S.  window  of  a  now  abandoned  stone  house,  the  N.W.  corner  of  which 
is  158  ft.  W.  and  193  ft.  S.  of  our  station.  The  house  is  a  one-story  struc- 
ture, having  the  dimensions  of  N.  and  S.  sides  18  ft.,  and  E.  and  W.  sides 
24  ft.  The  window  where  his  observations  were  made  is  in  the  middle  ot 
the  S.  side.  His  value  for  declination  in  18^9  was  9°  05'  E.  Our  value 
determined  June  22d,  1882,  was  7°  36' . 

Station  105  — In  Franklin  Co.  Lat.  38°  41';  Ion.  91°  20'.  The  sta- 
tion is  on  timber  land  of  Elijah  Ruck,  315  ft.  N.  and  15  E.  of  the  well  in 

*  Trans,  iv,  3,  p.  454. 


5l8  TRANS.  ST.  LOUIS  ACAD.  SCIENCE. 

front  of  the  house  of  John  Bedts,  and  about  325  ft.  from  the  line  between 
Franklin  and  Gasconade  counties.  The  station  was  said  to  be  in  sec.  10, 
tp.  45,  r.  4  W.     Polaris  obs.  on  elongation. 

Station  ig6  — /w  Gascovade  Co.  Lat.  38°  37';  Ion.  91°  29'.  On  the 
land  belonging  to  Fred.  Bruhns.  a  quarter  of  a  mile  N.  and  260  ft.  E.  of 
the  S.W.  corner  of  sec.  19.  tp.  45,  r.  5  W.  The  station  is  on  the  bank  of 
First  creek.  The  value  for  declination  here  was  very  much  smaller  than 
at  surrounding  stations,  but  no  error  could  be  detected  in  our  work. 
Whether  the  discrepancy  was  due  to  some  minute  local  effect  or  not,  we 
could  not  remain  to  determine,  as  sickness  at  home  made  it  desirable  to 
reach  the  telegraph  as  soon  as  possible.  This  is  the  only  case  of  the  kind 
so  far  reached,  excepting  in  the  Iron  Mountain  region.  Two  Polaris  ob- 
servations were  made  on  elongation. 

Station  107— /«  Osage  Co.  Lat.  38°  28';  Ion.  91°  41'.  On  the  land 
of  Fritz  Kaldeweiher,  near  the  centre  of  the  S.E.  qr.  of  the  S.W.  qr.  of 
sec.  9,  tp.  43.  r.  7  W.  The  station  was  50  ft.  N.  and  33  ft.  W.  of  the  N.W. 
corner  of  Kaldeweiher 's  house.     Polaris  obs.  on  elongation. 

Station  ic8  —  Z/w«,  Osage  Co.  Lat.  38°  28' ;  Ion.  91°  50' .  Station 
on  L'Ours  creek*  on  the  Jefferson  city  road,  about  half  a  mile  from  town. 
The  S.E.  corner  of  James  N.  Clark's  yard  is  72  ft.  W.  and  68  ft.  S.  of  the 
station.     Polaris  obs.  on  elongation. 

Station  109— /«  Crt//rtway  Co.  Lat.  38°  43' ;  Ion.  92°  01' .  On  Little 
Auxvasse  creek  at  the  crossing  of  the  New  Bloomfield  and  Fulton  road, 
about  40  rods  S.W.  of  the  N.E.  corner  of  sec.  28,  tp.  46,  r.  10  W.  A  spring 
across  the  creek  and  just  at  the  ford  lies  N.  65°  E.  165  ft.  Polaris  obs.  on 
elongation. 

Station  no— Near  Stffhen.'C  Store,  Boone  Co.  Lat.  38*^  58' ;  Ion.  92° 
05'.  About  one  half  mile  S.  of  the  village.  The  old  Fulton  road  is  12  ft. 
W.  and  the  bank  of  Cedar  creek  is  105  ft.  N.     Polaris  obs.  on  elongation. 

Station  hi  —  Cetiiralia,  Boone  Co.  Lat.  39°  13';  Ion.  92°  05'.  The 
station  was  on  a  vacant  lot  48  ft.  W.  of  the  centre  of  the  street  leading 
directly  S.  to  the  depot  and  crossing  of  the  Chicago  &  Alton  R.R.,  which 
is  about  a  square  and  a  half  distant.  The  centre  of  the  street  to  the  N.  is 
distant  77  ft.  and  leads  E.  to  a  flouring  mill,  the  smokestack  of  which  bears 
S.  90°  44'. 1  E.     Polaris  obs.  on  elongation. 

Station  112  —  In  Monroe  Co.  Lat.  39°  24';  Ion.  92°  10'.  On  the  S. 
bank  of  the  Long  Branch  of  Salt  river.  The  station  was  150  ft.  from  the 
creek  and  midway  between  the  road  and  the  W.  fence.  The  station  is  on 
the  W.  line  of  sec.  20,  tp.  53.  r.  ii-  W.,  and  about  120yds.  from  the  middle 
of  this  line.  Polaris  obs.  on  elongation.  —  Some  years  since  the  county 
surveyor  of  Audrain  Co.  called  my  attention  to  this  region  as  showing 

*  Named  after  the  first  (French)  settler  on  its  bunks.  A  postoffice  ne.ir  the  stream  was 
afterwards  named  "  Loose  Creek"  P.  O.  by  some  poor  speller,  and  this  official  name  has 
since  been  applied  to  the  stream,  which  appears  on  some  maps  as  "  Loose  Creek." 


NIPHER 5'^'^  ANN.  REP.  MAGNETIC  SURVEY  OF  MISSOURI.      519 

marked  local  effects.  The  region  is  level  prairie,  and  long  N.  and  S.  lines 
run  bj  compass  aregreatlj  and  uniformly  curved,  showing  an  abnormally 
great  easterly  declination.  This  station  and  station  No.  144,  about  12 
miles  E.,  show  an  area  of  abnormal  easterly  declination.  The  disturbed 
region  extends  over  an  area  of  many  miles. 

Station  iiT^—Moberly,  Randolph  Co.  Lat.  39°  26';  Ion.  92°  26'.  On 
the  fair  grounds  184  ft.  E.  and  2S9  ft.  S.  of  the  W.  entrance.  Polaris  obs. 
on  elongation. 

Station  114  —  Macon,  Macon  Co.  Lat.  39°  46';  Ion.  92°  30'.  In  the 
stock-yard  of  O.  S.  Bearce,  directly  in  front  of  his  barn  and  20  ft.  from  the 
Vine-st.  fence.  The  city  school-house  is  one  square  W.  and  one  square  N. 
Polaris  obs.  on  elongation. 

Station  115 — In  Macon  Co.  Lat.  39°  48';  Ion.  92°  37'  On  the  farm 
of  Isaiah  Lewis,  which  is  the  N.  halfof  N.E.  qr.  of  sec.  21,  tp.  58,  r.  15  W. 
The  station  was  in  front  of  the  house,  and  midway  between  the  road  and 
the  yard  fence.     Polaris  obs.  on  elongation. 

Station  116 — Near  Mercy ville,  Macon  Co.  Lat.  39°  57';  Ion.  92°  42'. 
About  half  a  mile  N.  of  town.  A  corner-stone  in  the  road,  a  quarter  of  a 
mile  S.  of  the  middle  point  of  the  N.  line  of  sec.  35,  tp.  60,  r.  16  W.,  bears 
S.  3°  23'  W.  589  ft.     Polaris  o-bs.  on  elongation. 

Station  117 — In  Linn  Co.  Lat.  39°  54';  Ion.  93°  07',  In  the  bottom 
of  the  west  branch  of  Yellow  creek.  The  station  is  within  a  few  feet  of 
the  corner,  a  quarter  of  a  mile  due  E.  of  the  middle  point  of  the  E.  line  of 
sec.  22,  tp.  59,  r.  19  W.  A  large  white-oak  tree  stands  20  ft.  W. ,  and  the 
east  end  of  the  bridge  is  261  ft.  distant.  The  mark  used  was  an  iron  rod 
on  the  bridge,  11  ft.  west  of  the  centre  of  the  bridge.  Polaris  obs.  on 
elongation. 

Station  118  —  Linnczus,  Linn  Co.  Lat.  39°  51';  Ion.  93°  13'.  On  a 
vacant  lot  on  the  summit  of  the  hill  E.  of  the  Burlington  &  South-western 
R.R.  depot.  The  S.  line  of  the  yard  of  Chas.  B.  Purdin  lies  166  ft.  N.,  the 
N.  line  of  the  farm  of  Joel  Wilkinson  lies  166  ft.  S.,  while  the  field  to  the 
E.  across  the  road  is  237  ft.  distant.  The  court-house  spire  was  used  as  a 
mark.     Two  polaris  observations  on  elongation. 

Station  119  —  Near  Laclede,  Linn  Co.  Lat.  39°  47';  Ion.  93°  17'. 
Station  one  mile  W.  of  town,  on  the  E.  side  of  Muddy  creek;  about  350  ft. 
E.  of  the  bridge  and  20  ft.  N.  of  the  road  centre.  The  station  is  said  to  be 
on  the  S  E.  qr.  of  sec.  36,  tp.  58,  r.  21  W.     Polaris  obs.  on  elongation. 

Station  120  —  /«  Livingston  Co.  Lat.  39°  38';  Ion.  93°  45' .  On  the 
farm  of  Wm.  E.  Wolfort,  in  the  N.E.  qr.  of  the  S.E.  qr.  of  sec.  33,  tp.  56,  r. 
25  W.  The  station  was  in  the  cattle-yard  25  ft.  from  the  road  fence  to  the 
east  (the  road  being  on  the  section  line),  and  40  ft.  N.  of  the  door-yard 
fence.  The  middle  line  of  the  section  is  in  the  E.  and  W.  road  perhaps, 
100  ft.  N.     Polaris  obs.  on  elongation. 

Station  121 — Kingston,  Caldwell  Co.  Lat.  39°  41';  Ion.  94°  04'.  The 
station   will  be  found  by  going  from   the  S.W.  corner  of  the  court-house 


520  TRANS.  ST.   I.OUIS  ACAD.   SCIENCE. 

square  W.  1646  ft.,  and  S.  from  the  middle  of  the  road  62  ft.  It  lies  91  ft, 
E.  of  the  summit  of  the  small  ridge.     Polaris  obs.  on  elongation. 

Station  122  — /«  Caldwell  Co.  -Lat.  39°  39';  Ion.  94°  11'.  On  land 
of  Christian  Smitt,  50  ft.  W.  and  212  ft.  N.  of  the  middle  of  sec.  29,  tp.  56, 
r.  29  W.     Polaris  obs    on  elongation. 

Station  i2-x,—Maysville,  DeKalb  Co.  Lat.  39°  43';  Ion.  94°  24'.  On 
the  grounds  of  the  public  school  building,  65  ft.  W.  and  21  ft.  N.  of  the 
N.W.  corner  of  the  building.     Polaris  obs.  on  elongation. 

Station  124—  /«  DeKalb  Co.  Lat.  40°  01' ;  Ion.  94°  23'.  On  land  of 
Harvey  Johnson,  50  ft.  S.  and  206  ft.  E.  of  the  middle  of  the  N.  line  of  sec. 
14,  tp.  60,  r.  31  W.     Polaris  obs.  on  elongation. 

Station  125  —  Albany.,  Getiiry  Co.  Lat.  40°  15';  Ion.  94°  21 ' .  The 
station  is  979  ft.  E.  of  the  N.E.  corner  of  the  court-house  square  and  8  ft. 
S.,  these  measurements  being  along  the  streets.  The  station  is  11  ft.  W. 
and  8  ft.  S.  of  the  N.E.  corner  of  lot  2,  block  5,  of  Hundley's  second  addi- 
tion.    Polaris  obs.  on  elongation. 

Station  126— /«  Getitry  Co.  Lat.  40°  16';  Ion.  94°  17'.  The  fence 
E.  on  the  E.  edge  of  sec.  15,  tp-  63,  r.  30  W.,  is  107  ft.  distant.  The  fence 
S  ,  which  is  the  S.  line  of  the  N.  half  of  the  N.E.  qr.  of  the  section,  is  193 
ft.  distant.  There  appears  to  be  a  double  corner  here.  The  evening-mark 
reading  was  missed,  but  the  station  was  on  raw  prairie  and  the  instrument 
was  certainly  not  disturbed  between  the  star  observation  and  the  morn- 
ing mark  reading.     Polaris  was  observed  on  elongation. 

Station  127 — Bethany,  Harrisofi  Co.  Lat.  40°  16';  Ion.  94°  03'.  On 
a  vacant  lot  of  Mrs.  R.  J.  Turner,  365  ft.  E.  of  the  N.E.  cornerof  her  house. 
The  station  is  about  320  ft.  S.  of  the  N.  line  and  346  ft.  W.  of  the  E.  line  of 
sec.  15,  tp.  63,  r.  28  W.  The  line  fence  of  T.  B.  Shearer's  yard  is  loi  ft. 
E.     Polaris  obs,  on  elongation. 

Station  128  —  Farm  of  John  Honafi,  in  Harrison  Co.  Lat.  40°  08'  ; 
Ion.  93°  56'.  The  station  was  in  the  meadow,  133  ft.  S.  and  289  ft.  W.  of 
the  N.E.  corner  of  sec.  36,  tp.  62,  r.  27  W.  Meridian  determined  by  equal 
altitudes  of  the  sun.  Small  cumulus  clouds  cut  oft"  five  observations  out  of 
a  series  of  seven.     The  two  differed  1 ' . 

Station  i2()— In  Daviess  Co.  Lat.  40°  04';  Ion.  93°  53'.  The  station 
was  in  the  road  about  midway  between  the  track  and  the  S.  fence,  and  334 
ft.  E.  of  the  N.W.  corner  of  the  S.  half  of  the  S.W.  qr.  of  sec.  28,  tp.  61, 
r.  26  W.  By  reason  of  a  very  heavy  rain  which  came  up  while  the  camp 
was  being  made  it  was  impossible  to  get  an  evening-mark  reading.  The 
rain  lasted  until  9:15  p.m.,  and  then  a  small  patch  of  sky  cleared  around 
polaris  for  about  half  an  hour,  and  a  pole-star  observation  was  made.l 

When  the  star-observation  was  made  the  whole  hillside  was  covered 
with  a  sheet  of  water  three  to  four  inches  inches  in  depth,  which  filled  the 
trenches  around  the  tent  and  ran  through  the  tent  in  a  torrent.  The 
ground  was  however  firm,  and  the  tripod  was  as  usual   mounted  firmly  on 


NIPHER 5"'  AW.  REP.  MAGNETIC  SURVEY  OF  MISSOURI.       52I 

large  stakes  driven  eight  to  ten  inches  into  the  ground.  The  observation 
was  therefore  deemed  entirely  satisfactory.  At  the  next  station  on  the 
next  night  an  observation  was  made  the  same  interval  before  elongation, 
and  the  difierence  between  the  azimuth  of  the  star  and  that  of  elongation 
agreed  within  a  quarter  of  a  minute  with  that  at  Station  129. 

Station  130 — Trenton^  Grufidy  Co.  Lat.  40°03';  Ion.  93°  39' .  Sta- 
tion in  a  grove  of  Dr.  Harris,  in  the  east  part  of  town.  The  station  is 
found  by  starting  at  the  front  (S.)  fence  of  the  door-yard  and  measuring 
S.  along  the  centre  of  the  road  112  ft.,  thence  E.  415  ft.  Polaris  obs.  on 
elongation. 

Station  131  —  In  Grundy  Co.  Lat.  40°  13';  Ion.  93°  38'.  Station  in 
the  road  about  midway  between  the  track  and  theE.  fence,  and  150  ft.  S.W. 
from  the  front  gate  of  the  farm  of  Faust  Amick.  The  station  is  near  the 
S.E.  corner  of  the  N.E.  qr.  of  N.E.  qr.  of  sec.  34,  tp.  63,  r.  24  W.  Po- 
laris was  observed  before  elongation,  and  its  azimuth  calculated  as  before 
described. 

Station  132 — Princeton.  Mercer  Co.  Lat.  40°  24' ;  Ion.  93°  39' .  The 
station  is  at  the  base  of  the  bluff,  395  ft.  W.  of  the  W.  side  of  Lincoln  st. 
and  563  ft.  N.  of  the  centre  of  Hickland  st.  Polaris  observations  were 
made  at  9  and  I2h.  30  m. 

Station  133 — In  Putnajn  Co.  Lat.  40°  27';  Ion.  93°  21'.  On  land  of 
Joseph  Williams,  about  a  quarter  of  a  mile  W.  of  the  centre  of  sec.  7,  tp, 
65,  r.  21  W.  The  station  was  about  20  ft.  N.  of  the  centre  of  the  road,  and 
250  ft.  E.  of  the  front  gate  of  the  house  of  Crede  Yocum.  Polaris  obs.  on 
elongation. 

Station  134 — Iti  Putnam  Co.  Lat.  40°  27';  Ion.  93°  21'.  Station  in 
a  lane  near  the  house  of  Joseph  Ward,  in  sec.  12,  tp.  65,  r.  20  W.  The 
middle  stone  of  the  S.  line  of  the  section  is  1S9  ft.  S.  of  the  station.  Pola. 
ris  observed  at  11  o'clock  p.m. 

Station  135 — Unionville.,  Putnam  Co.  Lat.  40°  29';  Ion.  93°  03'.  The 
station  is  on  an  open  square  562  ft.  N.W.  of  the  W.  corner  of  the  court- 
house square  and  150  ft.  N.W.  of  the  same.  These  measurements  are 
made  along  the  streets  which  lie  diagonally  in  reference  to  the  points  of 
the  compass.  The  sky  was  again  cloudy  at  elongation,  and  polaris  was 
observed  at  9  h.  11  m.  and  10  h.  46  m. 

Station  136  —  In  Sullivan  Co.  Lat.  40°  19';  Ion.  93°  07'.  On  the 
farm  of  Nathan  Bankes,  on  the  N.E.  qr.  of  the  S.E.  qr.  of  sec.  28,  tp.  64, 
r.  19  W.  The  station  is  in  the  meadow  26  ft.  S.  of  the  S.W.  corner  of 
Bankes'  house  and  249  ft.  W.  of  the  middle  of  the  road.  Polaris  obs.  on 
elongation. 

Station  137  —  Milan,  Sullivan  Co.  Lat.  40°  12'  ;  Ion.  93°  11'.  On 
the  common,  160  ft.  S.  of  the  S.W.  corner  of  the  public  school  building. 
Polaris  obs.  on  elongation. 


522  TKANS.  ST.  LOUIS  ACAD.  SCIENCE. 

Station  138 — Stickhrville,  Sullivan  Co.  Lat.  40°  09'  ;  Ion.  92°  58'; 
Near  the  S.W.  corner  of  the  N.W.  qr.  of  sec.  22,  tp.  62,  r.  18  W.  The  N. 
W.  corner  of  the  church  bears  S.  31°  15'  W.,  and  is  distant  731  ft.  The 
same  corner  of  the  church  is  137  ft.  S.E.  of  the  qr.  sec.  corner  before  men- 
tioned.    Polaris  obs.  not  at  elongation. 

Station  139  —  Kirksville^  Adair  Co.  Lat.  40°  12'  ;  Ion.  92°  37'.  In 
a  vacant  lot,  owned  by  Dr.  Hurley,  on  the  S.W.  corner  of  Fifth  and  Fill- 
more sts.,  76  ft.  from  the  centre  of  the  latter  and  83  ft.  from  the  centre  of 
the  former  street.  The  left  side  of  the  tower  of  the  State  Normal  school 
building  bears  S.  69°  02'.  5  E.     Polaris  obs.  on  elongation. 

Station  140 — La  Plata,  Macon  Co.  Lat.  40°  00' ;  Ion.  92°  34' .  Sta- 
tion in  the  street  about  midway  between  the  track  and  the  N.  fence.  The 
middle,  E.  and  W.  line  of  sec.  7,  tp.  60,  r.  14  W.,  is  486  ft.  N.,  and  the  E. 
line  of  the  section  is  637  ft.  E.  These  distances  were  measured  along  the 
streets.  The  house  of  B.  F.  Bragg  is  on  the  S.  side  of  the  street,  a  little  E. 
of  the  station.     Polaris  obs.  on  elongation. 

Station  141 — In  Macon  Co.  Lat.  39°  53'  ;  Ion.  92°  22'.  Station  on 
Bear  creek  bottom,  304  ft.  N.  and  832  ft.  E.  of  the  middle  of  the  S  line  of 
sec.  23,  tp.  59,  r.  13  W. ,  near  Harris's  farm.  Some  error  was  made  in 
reading  the  verniers  in  the  star  observation.  It  is  conjectured  that  the 
altitude  was  read  too  high  by  lo'.  This  conjecture  is  baesd  on  observa- 
tions at  the  next  station,  made  at  elongation  and  an  equal  interval  after 
elongation,  allowance  being  made  for  the  change  in  latitude. 

In  the  magnetic  determination  on  the  morning  of  the  12th  marked  dis- 
turbances of  the  needle  were  observed.  The  declination  diminished  9' 
between  6  and  7  o'clock. 

Station  142 — In  Shelby  Co.,  3  miles  S.  of  Shelby ville.  Lat.  39°  44'  ; 
Ion.  92°  04'.  The  middle  stone  on  the  N.  line  of  sec.  5,  tp.  57,  r.  10  W., 
bears  N.  4°,  50'  E.,  and  is  distant  910  ft.     Polaris  obs.  on  elongation. 

Station  143 — In  Monroe  Co.,  on  the  farm  of  Henry  Winkler,  40  ft.  E. 
of  the  centre  of  the  road,  and  669  ft.  N.  of  the  S.  line  of  sec.  35,  tp.  56,  r. 
10  W.  The  road,  which  runs  N.  and  S.,  divides  the  S.W.  qr.  of  the  sec- 
tion in  halves.     Polaris  obs.  on  elongation. 

Station  144 — In  Monroe  Co.  Lat.  39°  22'  ;  Ion.  91°  59'.  On  the 
summit  of  the  S.  bluff  of  Long  Branch  of  Salt  river,  W.  of  the  road,  on 
land  of  B.  F.  Dowell.  The  land  is  in  sec.  30,  tp.  53,  r.  9  W.  The  station 
was  about  75  ft.  W.  of  the  road,  which  is  on  the  E.  line  of  the  section. 
The  Baptist  church  across  the  road  is  about  50  ft.  farther  S.  than  the  sta- 
tion. These  measurements  were  forgotten,  and  the  distances  were  esti- 
mated the  same  day  after  having  left  the  locality.  Polaris  observation  on 
elongation. 

Station  145 — Montgomery  City,  Lat.  39°  00' ;  Ion.  91°  30' .  The  sta- 
tion is  105  ft.  W.  of  the  middle  (N.  and  S.)  line  of  the  S.E.  qr.  of  sec.  32, 
tp.  49,  r.  5  W.,  and  a  perpendicular  laid  off  to  the    track  of  the    Wabash- 


NIPHER 5^''  ANN.  REP.   MAGNETIC  SURVEY  OF  MISSOURI.       523 

Pacific  R.R.  track  measures  200  ft.  Passing  freight  trains  caused  the  nee- 
dle to  swing  through  2'.     Polaris  obs.  on  elongation. 

Station  146  —  Warrenton,  Warren  Co.  Lat.  38°  46'  ;  Ion.  91°  08' . 
The  station  is  at  theW.  end  of  town,  about  a  mile  from  the  station  of  1881. 
Starting  at  the  creek  bridge  W.  of  the  court-house,  the  station  will  be  found 
bj  going  along  the  road  westwardlj  705  ft.,  thence  southwardly  at  right 
angles  to  the  road  a  distance  of  45  ft.  The  court-house  spire  bears  S.  79° 
14.3'  E.     Polaris  obs.  on  elongation. 

Station  147— /«  St.  Charles  Co.  Lat.  38°  43';  Ion.  90°  40'.  The  sta- 
tion is  in  the  Booneslick  road  about  midway  between  the  track  and  the  S. 
fence,  and  almost  due  south  of  O'Fallon.*  The  O'Fallon  road  is  250  ft.  E. 
The  house  of  D.  Heald  lies  a  few  rods  to  the  W.  Polaris  observation  on 
elongation. 

Station  148—///  St. Louis  Co.  Lat.  38°  41';  Ion.  90°  21'.  On  the  St. 
■Charles  rock  road.  The  station  was  in  a  gap  in  the  fence  opposite  the 
grounds  of  J.  B.  Lucas.  From  the  station  to  the  centre  of  the  road  the 
distance  is  30  ft.  From  thence  along  the  road  to  a  point  opposite  the  gate 
is  165  ft.,  while  the  distance  in  the  opposite  direction  to  a  point  opposite 
the  S.E.  corner  of  the  Lucas  grounds  is  158  ft.  Polaris  observation  on 
elongation. 

Station  149 — Near  Atalissa,  Muscatine  Co.,  Iowa,  on  the  farm  of  Mrs. 
Grace  Aikins,  on  the  N.E.  qr.  of  the  N.W.  qr.  of  sec.  3,  tp.  78,  r.  3  W. 
The  station  is  on  the  front  path,  exactly  between  the  front  gate  and  the 
house.  This  station  is  a  mile  west  of  station  33  in  the  report  of  i88o.t 
Polaris  obs. 

Station  34 — This  station  was  occupied  in  1880,  and  is  described  in  the 
report  for  that  year.     Polaris  obs.  on  elongation. 

At  six  of  the  stations  of  the  summer  deflection  determinations 
were  made  with  the  University  magnetometer,  with  magnet  Cg 
deflecting  and  Cj^  deflected,  and  these  observations  have  been 
used  in  determining  the  value  of  P.,  and  in  calculating  the  mag- 
netic moment  of  Cg  for  the  summer.  The  latter  was  sensibly 
constant,  the  observed  diflerence  between  the  extreme  value 
observed  and  the  mean  of  all  being  about  o.^q^j,  of  the  average 
moment.  In  the  reduction  of  the  work  the  magnetic  moment 
was  therefore  assumed  to  be  constant.  The  calculations  for  P 
and  for  the  magnetic  moment  are  given  in  the  adjoining  tables. 

*  In  the  report  for  iSSo  the  Ion.  of  O'Fallon  should  be  99'  40'. 

t  Station  33  is  on  the  N.E.  qr.  of  the  N.W.  qr.  of  sec.  2,  and  not  N.E.  qr.  of  N.E.  qr. 
as  was  given  in  the  report  of  1 5S0. 


524 


TRANS.  ST.  LOUIS  ACAD.  SCIENCE. 


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NIPHKR — 5*''  ANN.  REP.  MAGNETIC  SURVEY  OF  MISSOURI.      525 

The  value  of  P^  as  determined  in  the  first  of  the  tables,  gives 
p 
for  the  value  of  i ^  the  values 

P  , 

I     —  ^  =    0.9946  log    =    9-99765 

_  ^  —  1  — 

I  /j  \2     —     0.9930  ^^^  9*9  96  9  5 

These  values  were  used   in  the  reduction  of  the  deflection  series 
made  for  the  determination  of  the  magnetic  moment  of  magnet 

In  the  second  table,  the  decrease  (a)  in  the  value  of  log  m  is 
determined,  and  it  is  found  that  for  the  summer  of  1882,  and  at 
a  temperature  of  80.7,  the  value  of  {a)   is 


'^•000,009' 
20  32 


or  \o^m   =    9.86415    +   O-000,009    ^' 

where  d  is  estimated  in  days  from  July  13.     The  value  of  log  m 

was  therefore  considered  constant  during  the  summer. 

In  all  of  the  intensity  determinations  the  time  of  vibration  was 
determined  by  means  of  a  Waltham  watch  belonging  to  Mr. 
Ringling.  This  watch  had  been  cleaned  just  before  leaving  St. 
Louis,  but  it  had  not  been  rated.  The  error  of  the  watch  was 
determined,  at  intervals  during  the  summer,  by  comparison  with 
clock-beats  from  the  observatory  of  Washington  University, 
transmitted  daily  to  the  telegraph  lines  of  various  railways  in  the 
State.  Its  rate  during  the  summer  was  a  loss  of  20  seconds  per 
day,  fluctuating  however  between  17  and  22  seconds.  The  cor- 
rection on  the  time  of  vibration  was  -(-  o.qqj6  second  at  all  the 
stations,  the  time  of  vibration  at  the  stations  not  varying  suffi- 
ciently to  change  the  value  of  this  correction.  The  effect  of 
neglecting  this  correction  altogether  would  be  equivalent  to  the 
effect  of  an  error  of  half  a  degree  in  temperature. 

The  intensity  determinations  were  all  made  with  magnet  Cg  in 
the  University  declinometer,  C  j  7  being  used  as  a  deflected  mag- 
net. The  moment  of  inertia  of  Cg  was  obtained  from  the  table 
given  in  the  4th  report.*     The  values  for  H  ?lx&  not  corrected  for 

*  Trans,  vol.  iv.  No.  3,  p.  468. 


526 


TRANS.  ST.  LOUIS  ACAD.   SCIENCE. 


the  effect  of  magnetic  brass-work  of  the  magnetometer.  This 
correction  is  given  in  the  4th  report,  p.  472. 

The  observations  for  inclination  were  not  very  satisfactory,  as 
the  axes  of  the  needles  were  both  bent  during  the  early  part  of 
the  summer. 

The  following  observations  for  meridian,  by  equal  altitudes  of 
the  sun,  were  made.  The  method  of  reduction  has  been  ex- 
plained in  previous  reports. 

Sun  Observations  for  Meridian. 


Station. 

Date. 

X3 
0 

0 

6 

Mean  Time  of  Series. 

i. 

}i(A+A'). 

A.  M. 

p.  M. 

Little  Auxvasse  Cr. 
Honan's 

June  30 
July  30 

5 
2 

k.  m.   s. 

9  36  58 
9  38  25 

A.   m.   s. 

2  32   40 
2    23    18 

deg.    m. 

37  03.7 

35  42-5 

deg.     m. 

244   56.7 
176   38.5 

log  A  d". 

a.  c.  log  cos 

a.c.  log  sin  t 

Cor. 

South  reads 

Mark  reads 

Az.  of  Mark. 

I.67112 
2.23805 

0.10777 
0.11660 

0.21992 
0.23384 

4-o'.8 
+  3-2 

244°57'-5 
176  41  .7 

l80°02^0 
180   01   .2 

S.64°55-5E. 
S.    3   19.5  W. 

Polaris  Observations  for  Meridian. 


Station. 


Daviess  Co.,    Sta.  129. 
Amick's 


Princeton 


Ward's  . . . . 
Unionville. 


Sticklerville 
Harris's  . . . . 


Lat.  <p. 


40'='  04' 
40  13 

40  24 

(( 

40  27 
40  29 

40  09 
39  53 


Alt.  /^.* 


39°  42'' -5 

39  34  -o 

39  46  .0 

39  58 

40  05 
40  48 
40  12 
40  45 
39  37  -o 

39  46  -5 

40  25  .of 


Polar  D./. 


19^-3 


^  Sum  =S. 


40°  32/. 9 

40  33-1 
40  39  .2 
40  50  .6 
40  54  .2 
17  .2 


41 

41  00 

41  16 

40  32 

40  37 


40  48  .6 


*  The  altitudes  are  all  corrected  for  refraction. 

f  This  altitude  was  recorded  40''  36'. o.  It  should  have  been  40*  26I ,  as  was  deter- 
mined at  the  next  station  (Shelbyville)  by  an  observation  made  the  same  time  interval  after 
elongation. 


NIPUER 5^'^  ANN.    REP.   MAGNETIC  SURVEY  OF  MISSOURI.      537 


J3 

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528 


TRANS.  SI  .  LOUIS  ACAD.  SCIENCE. 


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■^  Jr^  M  t^OO  t^"   ro-^rot^ioiorO  —  so   msDsO    -^CO  I>. 

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OS  -^so   ^  <X>  OVO  t^LOOsOsOsrow   ■^lo  t(-oo  m  CC   >-.  00 

1-1  OssD  rO  M  t^  t^sO  M  O  OSN  fOrOM  O  fS  M  rit^tort- 
roO  LoO  -^r^Loo  "-tjO  roroO  O  ►-'  CH  loc^  n  n  ro-^ 
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10  t^  roCO   0\C0   "   PO  "-o  -^  r^sO  sO   -^Ni—  (NvosO   Th  osoo 

t^O   >^OCO00   M    loO  X>.00   O   "J-'M   toJr^trjM  t^O  t^l>- 

CJN  rooo  ThN  j>.i-i  t-i-H  000  MIX  Tt-roOS'^r<  Thw  ir-.vo 
(siwioO'^roOOLoOrorO'^.  O'-'i-'LoNDrorO'^ 
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rOOO  10  CO  O  N  O  00  M  ■^00  fODsO  i-isOOOCOOOOOJ^-lo 
LO  !>.  roOO  OsOO  N  fO  Lo  ■^  t^vo  SO  -^rir^oivo^  ■^  OsOO 
MM         MHiMroMMCOMtr)        Mi-ii-it-i  M         M 

NSO   Osoo   O  00  so  00   Lo  N    >-i    OsOO   H-i    woo   i-i\0   lOMVD    OS 

MfOi-iOOOroOi-iO'-i--i-i-<>HOMOMroOi-i 

+  i  I  I      II  !+++++!  I +  1  +  1  I  I  I 

^N   M   N   M   c>   r<   N   OsosOsOsCTsOsOsOsOsw   >-i   —   w  '^ 

§)00oocooocoooco  t^t^t^t^t^j^-t^t^  t^co  co  00  00  00 

I I      I ^1 — ji ^1 I       I II — ^1 ^1 ^1 ^1 — II ii I      1 ^1 II II I 

crj  fO  M  00   M  00   fOOO  t^  O   lo  OS  -"^  PO  ro  roOO  lOCO   ■^00   11 

"osSO  t^  J>-00  1>.\0  t~-00  00  00  00  O  t^  t^OO  so  00  so  so  i^  t>. 

__  -_ 

ri         wirj        OS  Os-^«o       "^  co       t^co        ■<i-0 

_3*      ••*      •**      •••*      .**      .*      ..*      .. 
vo         •<j- Lo        Trh  vo -"^  Th        t^  vo        loco        Th  CO 


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On  0\  OnOO  OOOOCOCOOOCCOOOOCOOO  t^OD  COOOOOCO  i>.t^t^t^  t^MD  MD  NO  t>-  *>•  t^ 
ONOf<Oc)i^OroOS'^  Tj-00   wCOOOCJO    0\0   "OCS    OnO   logo    i-i  CO    -^  ro  M  CO   ■<*■ 

row  rOCJ  fO-^'^Tt-O  (S  -rt-cots  O'orO'-i  •^m  O  ro■^■^'J^O  rO-^O  M  m  •<*• 
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VO  O  <^  rO  -^00  t^  Ov  Ov  t>-  ^OvO  00  -OvOO  O  t--vb  M  6  OwO  On  i-<  >-o  ro  O  O  »^  J>.VO 
M   Tt-\o   MJ:^Oi-OOM^»^^'f»|-'i-iJ>-OM'*  'i-vo  vO   O   O    '-   >^OvOM:-»tr"" 

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<U      •      •      •    (U  1)  ...(Ij.... 

en  tc  tc  <"■___ 

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OOOOLoioO        OCO       iOOO^oOOOO       ::ooo         •ooo 

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00  00  00  00  >-■  r^co  o(»oooo5      000000  t^co  cococoS      cocoooo    -oooooo 

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lo  M   fO  •-  CO   w-iCO  J>-'*-Loro       OOt^t^O'^LO'J^t^rO  00  l>.VO  vO  vO   "1  lOOO 

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I +  I  I  I  I  I  + 1  I  I  I  +  r+ 1  I  I  I  + 1 ++++++ 1  + 1 

OvCvOvOvOvOvOvOvOnOvOvOv  OvvO  vCvOvOvOvOvOvOvOvOvOvOvOvOVOCOOOOO 

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53' 


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TRANS.  ST.  LOUIS  ACAD.  SCIENCE. 


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■+•■^"^■<j-4•■<5-^•4-'^4-'^'^'*-4-TJ-TJ-T^Tl-Ti-■<J-Tt- 


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t^OO  CO   t^  t^  1>.\0  \OvD   Low-ivO^^    LOU-,  ly^LOLow-)!/-, 

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M   N   r)   M   M   (S   (N   fj   n   "^i   r>   n   n   M   M   M   N    M   M   fs   r> 
N   n   M   n   n   (-1   M   r«   M  n   n   D   M   r)   M  n   M  (S  (S   N   'I 


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TRANS.  ST.  LOUIS  ACAD.  SCIENCE. 


INCLINATION,  OR  DIP. 

Needle  No  2. 


STATION. 


Marked  End. 


North. 


South. 


Means   by  Polarities. 


Series  I.    Series  II. 


Resulting 
Dip. 


Date. 


Kirkwood*.. 

Goebel's 

Linn 

Little  Anxvasse  Cr'k 

Centralia 

Moberly 

Mercyville 

Linneus 

Wolfort's* 

Kingston ■ 

Maysville 

Albany 

Bethany 

Trenton 

Princeton 

Unionville 

Milan 


68^59;. 9 

66^44;.  9 

68  53 

.4 

69  18  .1 

68  35 

.0 

68  58  .8 

68  50 

.6 

69  19  ,5 

69  26 

.2 

69  48  .2 

65  25 

.2 

69  45  .4 

69  54 

.4 

70  07  .5 

69  51 

.4 

70  10  .0 

70  41 

.2 

71  07  .4 

70  04 

.8 

70  15  .4 

69  34 

.4 

69  51  .9 

70  04 

•6 

70  25  .4 

70  04 

.9 

70  29  .0 

70  04 

.8 

70  24  .8 

70  13 

.6 

70  30  .0 

70  23 

.6 

70  05  .4 

70  05 

.8 

70  27  .9 

G9°01;, 
68  58  , 
68  39 

68  54 

69  44 
69  30  . 
69  .57 

69  53 

70  34 
70  05 

69  33 

70  08  , 
70  12 
70  04 
70  16 
70  20 
70  10 


r66°48;,8 

6  69  12  .8 

0'68  54  .7 

5  69  15  .6 

6  69  29  .6 
l!69  37  .8 
0  70  04  .8 
0  70  08  .5 
9  71  13  .7 


70  14  .8 

69  52  .5 

70  21  .2 
70  21  .9 
70  25  .2 
70  27  .4 
70  08  .4 
70  23  .4 


67^52 i 
69  05 

68  46 

69  05 
69  37 

69  35 

70  00 
70  00 
70  54 
70  10 

69  43 

70  15 
70  16 
70  14 
70  21 
70  14 
70  16 


June  17 
"     22 

"     27 

''  3a 

July  5 

"  7 

"  11 

"  15 

"  20 

"  22 

"  24 

"  26 

"  27 
.8 'Aug.  1 

.8!     "  2 

.5      "  5 

.8,     "  8 


*  Some  error. 


Needle  No. 


STATION. 


Marked   End. 

Means   by 

Polarities. 

Resulting 
Dip. 

North. 

South. 

Series  1. 

Series  II. 

69«34».7 

69^^15 ;. 7   70  39 -.5 

68''10;.9 

69°25;.2 

69  19  .1 

68  48  .4  '  68  15  .8 

69  51  .6 

69  03  .7 

67  34  .8 

68  43  .8   68  23  .5 

69  55  .1 

69  09  .3 

69  ,54  .8 

69  18  .8   68  44  .3 

70  29  .3 

69  36  .8 

70  24  .6 

69  36  .4   69  04  .4 

70  56  .6 

70  00  .5 

70  21  .5 

69  45  .2|  69  08  .8 

70  57  .8 

70  03  .4 

70  03  .5 

69  30  .5   69  33  .2 

70  00  .8 

69  47  .0 

70  52  .9 

69  59  .8  i70  27  .8 

70  24  .9 

70  26  .4 

70  35  .6 

69  55  .9 

70  07  .4 

70  24  .2 

70  15  .8 

Kirkwood 

Goebel's 

Little  Auxvas.se  Cr'k, 

Moberly. 

Mercyville 

Linneus 

Maysville 

Bethany 

Trenton  


June  17 
"  22 
"     30 

July  7 
"11 
"  15 
"  24 
"     27 

Aug.   1 


NIPHER EXPRESSION  OF  ELECTRICAL  RESISTANCE,  ETC.       535 

On  the  Expression  of  Electrical  Resistance  in  Terms 
of  a  Velocity. 

By  Francis  E.  Nipher.* 

If  a  spherical  shell  of  radius  r  be  charged  with  Q  units  of  elec- 
tricity, the  density  of  electrification  being-  p  ^  the  force  dF  over 
any  element  ds  of  its  surface  will  be  2  k  p^ds.  This  force  is  di- 
rected radially  outward,  and  is  due  to  the  action  of  the  electrifi- 
cation Q  on  the  quantity  pds  upon  the  element. 

If  the  radius  r  be  diminished  to  r',  the  energy  of  the  electri- 
fication will  increase  if  Q  remains  constant,  this  increase  in 
energy  being  due  to  work  done  on  the  sphere  by  some  external 
source,  causing  the  sphere  to  collapse.  If  the  element  ds  sweeps, 
through  a  distance  dr,  the  stored  energy  will  be 

dE  =  dFdr  -        -        -        (i) 

in  which  both  dF  zxi^  dr  are  essentially  negative. 

Substituting  in  (i)  the  above  value  of  dF  and  remembering 

that  P  =  —    , 

and  ds  =  r^  du  , 

where  dw  is  the  solid  angle  subtended  by  the  element  ds.,  we  have 

dB  =  ^ ~^du 

OTv    r^ 

where  one  integration  is  carried  over  the  surface  of  the  sphere, 
anJ  the  other  is  carried  inwards  between  the  limits  r  and  r' . 
Performing  the  integrations,  we  have 


2 


I  r'  r   } 


I      O^ 
But—  —  is  the  energy  of  a  sphere  of  radius  r>  ^  charged  with 

Q  units  of  electricity,  and  hence  the  potential  of  the  sphere  on 
itself  between  the  limits  r  and  r'  is  equal  to  the  difference  in  its 
initial  and  final  energy. 

If  the  sphere  were  connected  with  the  ground,  by  a  wire  of  re- 
sistance (/?),  the  radius  (r)  might  be  changed  in  such  a  manner 

*  Read  March  17th,  18S4. 


r — r 


536  TRANS.  ST.  LOUIS  ACAD.  SCIENCE. 

as  to  preserve  the  potential  (  F)  constant.  In  this  case  a  current 
of  constant  intensity  would  flow  through  the  wire,  and  as  F=  — 
it  is  clear  that  r  must  change  at  a  uniform  rate,  or 

=  /'-/  -         -         -         (3) 

where  t'  —  /  is  the  duration  of  the  operation.     Further, 

Q  47rrV 

K  =  -^= =  477r/j 

r  r 

and  V     . 

^^"^^^  dE=dFdr=2TT  p2  dsdr=  —  drdo>  , 

or  V^    rr  V^ 

B-B'  =^jC/drdo>=-^  (r-r')         .  .  (4) 

This  is  the  stored  energy  during  the  operation.  But  the  energy 
of  the  electrification  at  first  was  h  r  V^,  and  at  the  end  is  2  r'  V^, 
so  that  there  has  nevertheless  been  a  diminution  of  energy  of 

B  —  B'=~(r—r>)  ...  (5) 

It  appears  that,  under  conditions  of  our  experiment,  the  sphere 
has  less  energy  at  the  close  of  the  experiment  than  at  the  begin- 
nmg   by  a  quantity  —  (r —  r'),  while  the  equal  energy  repre. 

sented  by  the  potential  of  the  electrification  on  itself  was  added. 
The  total  energy  lost  by  the  shell  was,  therefore, 

jB  =    V^{r—r')  -  .  -  (6) 

The  current  in  the  wire  was,  by  Ohm's  law, 

dq_    F, 
^-  dt   -  ^  ' 
hence  ^       ^         V 

and  hence  the  energy  of  the  current  during  the  operation  was 

or  by   (3),  K'  r-r'  ■  _  _ 

R        V  ^'' 

The  expressions  (6)  and  (7)  must  be  equal  to  each  other,  and 

bence  Rv  =  x  ,        or        /?  =  -    , 

where  v  is  the  constant  velocity  of  each  point  in  the  surface  of  the 
shell  during  the  operation. 


i 


